4x^2-10x=500

Solution for 4x^2-10x=500 equation:

4x^2-10x=500

We move all terms to the left:

4x^2-10x-(500)=0

a = 4; b = -10; c = -500;
Δ = b2-4ac
Δ = -102-4·4·(-500)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-90}{2*4}=\frac{-80}{8}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+90}{2*4}=\frac{100}{8}
=12+1/2
$