8s^2-44s+60=0 — step-by-step solution

1) Let's solve in

ℝ

8 s^{2} - 44 s + 60 = 0

Since

4 \neq 0

, divide both sides by

4

2 s^{2} - 11 s + 15 = 0

Given the quadratic form

a s^{2} + b s + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 2

b = -11

and

c = 15

Δ = {(-11)}^{2} - 4 \cdot 2 \cdot 15

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{(-11)}^{2}

(-11) \cdot (-11)

121

■Multiplications are done before additions and subtractions:

4 \cdot 2

8

Δ = 121 - 8 \cdot 15

ⓘ Multiplications are done before additions and subtractions:

8 \cdot 15

8 \cdot (10 + 5)

8 \cdot 10 + 8 \cdot 5

80 + 40

120

Δ = 121 - 120

ⓘ Start from

121

and move back

120

on the number line:

121 - 120

1

Δ = 1

Δ > 0

, the equation has two roots:

The quadratic formula gives

s_{1}

\frac{- b - \sqrt{Δ}}{2 a}

\frac{- (-11) - \sqrt{1}}{2 \cdot 2}

s_{1} = \frac{11 - 1}{2 \cdot 2}

ⓘ The numerator and the denominator are computed before the division:

11 - 1

10

ⅰ

2 \cdot 2

4

s_{1} = \frac{10}{4}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{10}{4}

\frac{5 \cdot 2}{2 \cdot 2}

\frac{5}{2}

s_{1} = \frac{5}{2}

The quadratic formula gives

s_{2}

\frac{- b + \sqrt{Δ}}{2 a}

\frac{- (-11) + \sqrt{1}}{2 \cdot 2}

s_{2} = \frac{11 + 1}{2 \cdot 2}

ⓘ The numerator and the denominator are computed before the division:

11 + 1

12

ⅰ

2 \cdot 2

4

s_{2} = \frac{12}{4}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

4

, their greatest common divisor:

\frac{12}{4}

3

s_{2} = 3

▶Solutions found:

s = {\frac{5}{2}, 3}

2) The numeric value of:

s = {\frac{5}{2}, 3}

equals:

▷

s = {2.5, 3}