5x^2+48x-3200=0

Solution for 5x^2+48x-3200=0 equation:

5x^2+48x-3200=0

a = 5; b = 48; c = -3200;
Δ = b2-4ac
Δ = 482-4·5·(-3200)
Δ = 66304
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:

$\sqrt{\Delta}=\sqrt{66304}=\sqrt{256*259}=\sqrt{256}*\sqrt{259}=16\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{259}}{2*5}=\frac{-48-16\sqrt{259}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{259}}{2*5}=\frac{-48+16\sqrt{259}}{10}
$