0=4x^2-36x+59

Solution for 0=4x^2-36x+59 equation:

0=4x^2-36x+59

We move all terms to the left:

0-(4x^2-36x+59)=0

We add all the numbers together, and all the variables

-(4x^2-36x+59)=0

We get rid of parentheses

-4x^2+36x-59=0

a = -4; b = 36; c = -59;
Δ = b2-4ac
Δ = 362-4·(-4)·(-59)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{22}}{2*-4}=\frac{-36-4\sqrt{22}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{22}}{2*-4}=\frac{-36+4\sqrt{22}}{-8}
$