4x^2+5x=320

Solution for 4x^2+5x=320 equation:

4x^2+5x=320

We move all terms to the left:

4x^2+5x-(320)=0

a = 4; b = 5; c = -320;
Δ = b2-4ac
Δ = 52-4·4·(-320)
Δ = 5145
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:

$\sqrt{\Delta}=\sqrt{5145}=\sqrt{49*105}=\sqrt{49}*\sqrt{105}=7\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7\sqrt{105}}{2*4}=\frac{-5-7\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7\sqrt{105}}{2*4}=\frac{-5+7\sqrt{105}}{8}
$