4x^2+36x=320

Solution for 4x^2+36x=320 equation:

4x^2+36x=320

We move all terms to the left:

4x^2+36x-(320)=0

a = 4; b = 36; c = -320;
Δ = b2-4ac
Δ = 362-4·4·(-320)
Δ = 6416
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:

$\sqrt{\Delta}=\sqrt{6416}=\sqrt{16*401}=\sqrt{16}*\sqrt{401}=4\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{401}}{2*4}=\frac{-36-4\sqrt{401}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{401}}{2*4}=\frac{-36+4\sqrt{401}}{8}
$