80x+4x^2=325

Solution for 80x+4x^2=325 equation:

80x+4x^2=325

We move all terms to the left:

80x+4x^2-(325)=0

a = 4; b = 80; c = -325;
Δ = b2-4ac
Δ = 802-4·4·(-325)
Δ = 11600
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:

$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{29}}{2*4}=\frac{-80-20\sqrt{29}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{29}}{2*4}=\frac{-80+20\sqrt{29}}{8}
$