4(5x-3)5x+5=118

Solution for 4(5x-3)5x+5=118 equation:

4(5x-3)5x+5=118

We move all terms to the left:

4(5x-3)5x+5-(118)=0

We add all the numbers together, and all the variables

4(5x-3)5x-113=0

We multiply parentheses

100x^2-60x-113=0

a = 100; b = -60; c = -113;
Δ = b2-4ac
Δ = -602-4·100·(-113)
Δ = 48800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48800}=\sqrt{400*122}=\sqrt{400}*\sqrt{122}=20\sqrt{122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{122}}{2*100}=\frac{60-20\sqrt{122}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{122}}{2*100}=\frac{60+20\sqrt{122}}{200}
$