-117=-5x(4x-1)-2

Solution for -117=-5x(4x-1)-2 equation:

-117=-5x(4x-1)-2

We move all terms to the left:

-117-(-5x(4x-1)-2)=0


We calculate terms in parentheses: -(-5x(4x-1)-2), so:

-5x(4x-1)-2

We multiply parentheses

-20x^2+5x-2

Back to the equation:

-(-20x^2+5x-2)


We get rid of parentheses

20x^2-5x+2-117=0

We add all the numbers together, and all the variables

20x^2-5x-115=0

a = 20; b = -5; c = -115;
Δ = b2-4ac
Δ = -52-4·20·(-115)
Δ = 9225
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:

$\sqrt{\Delta}=\sqrt{9225}=\sqrt{225*41}=\sqrt{225}*\sqrt{41}=15\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15\sqrt{41}}{2*20}=\frac{5-15\sqrt{41}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15\sqrt{41}}{2*20}=\frac{5+15\sqrt{41}}{40}
$