2x2-75x+500=0

Solution for 2x2-75x+500=0 equation:

2x^2-75x+500=0

a = 2; b = -75; c = +500;
Δ = b2-4ac
Δ = -752-4·2·500
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{65}}{2*2}=\frac{75-5\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{65}}{2*2}=\frac{75+5\sqrt{65}}{4}
$