0=4x^2+5x-36

Solution for 0=4x^2+5x-36 equation:

0=4x^2+5x-36

We move all terms to the left:

0-(4x^2+5x-36)=0

We add all the numbers together, and all the variables

-(4x^2+5x-36)=0

We get rid of parentheses

-4x^2-5x+36=0

a = -4; b = -5; c = +36;
Δ = b2-4ac
Δ = -52-4·(-4)·36
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{601}}{2*-4}=\frac{5-\sqrt{601}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{601}}{2*-4}=\frac{5+\sqrt{601}}{-8}
$