8x^2-600x+5625=0

Solution for 8x^2-600x+5625=0 equation:

8x^2-600x+5625=0

a = 8; b = -600; c = +5625;
Δ = b2-4ac
Δ = -6002-4·8·5625
Δ = 180000
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:

$\sqrt{\Delta}=\sqrt{180000}=\sqrt{90000*2}=\sqrt{90000}*\sqrt{2}=300\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-300\sqrt{2}}{2*8}=\frac{600-300\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+300\sqrt{2}}{2*8}=\frac{600+300\sqrt{2}}{16}
$