7(s-1)(s+5)=s*2+4s-2

Solution for 7(s-1)(s+5)=s*2+4s-2 equation:

7(s-1)(s+5)=s*2+4s-2

We move all terms to the left:

7(s-1)(s+5)-(s*2+4s-2)=0

We add all the numbers together, and all the variables

7(s-1)(s+5)-(4s+s*2-2)=0

We get rid of parentheses

7(s-1)(s+5)-4s-s*2+2=0

We multiply parentheses ..

7(+s^2+5s-1s-5)-4s-s*2+2=0

We multiply parentheses

7s^2+35s-7s-4s-s*2-35+2=0

Wy multiply elements

7s^2+35s-7s-4s-2s-35+2=0

We add all the numbers together, and all the variables

7s^2+22s-33=0

a = 7; b = 22; c = -33;
Δ = b2-4ac
Δ = 222-4·7·(-33)
Δ = 1408
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-8\sqrt{22}}{2*7}=\frac{-22-8\sqrt{22}}{14}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8\sqrt{22}}{2*7}=\frac{-22+8\sqrt{22}}{14}
$