5x2-75-5x=0

Solution for 5x2-75-5x=0 equation:

5x^2-75-5x=0

a = 5; b = -5; c = -75;
Δ = b2-4ac
Δ = -52-4·5·(-75)
Δ = 1525
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:

$\sqrt{\Delta}=\sqrt{1525}=\sqrt{25*61}=\sqrt{25}*\sqrt{61}=5\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{61}}{2*5}=\frac{5-5\sqrt{61}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{61}}{2*5}=\frac{5+5\sqrt{61}}{10}
$