80+48x-4x^2=0

Solution for 80+48x-4x^2=0 equation:

80+48x-4x^2=0

a = -4; b = 48; c = +80;
Δ = b2-4ac
Δ = 482-4·(-4)·80
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{14}}{2*-4}=\frac{-48-16\sqrt{14}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{14}}{2*-4}=\frac{-48+16\sqrt{14}}{-8}
$