2x^2-480x=19175

Solution for 2x^2-480x=19175 equation:

2x^2-480x=19175

We move all terms to the left:

2x^2-480x-(19175)=0

a = 2; b = -480; c = -19175;
Δ = b2-4ac
Δ = -4802-4·2·(-19175)
Δ = 383800
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:

$\sqrt{\Delta}=\sqrt{383800}=\sqrt{100*3838}=\sqrt{100}*\sqrt{3838}=10\sqrt{3838}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-10\sqrt{3838}}{2*2}=\frac{480-10\sqrt{3838}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+10\sqrt{3838}}{2*2}=\frac{480+10\sqrt{3838}}{4}
$