5x^2-150x-5625=0

Solution for 5x^2-150x-5625=0 equation:

5x^2-150x-5625=0

a = 5; b = -150; c = -5625;
Δ = b2-4ac
Δ = -1502-4·5·(-5625)
Δ = 135000
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:

$\sqrt{\Delta}=\sqrt{135000}=\sqrt{22500*6}=\sqrt{22500}*\sqrt{6}=150\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-150\sqrt{6}}{2*5}=\frac{150-150\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+150\sqrt{6}}{2*5}=\frac{150+150\sqrt{6}}{10}
$