5(x-5)x=45

Solution for 5(x-5)x=45 equation:

5(x-5)x=45

We move all terms to the left:

5(x-5)x-(45)=0

We multiply parentheses

5x^2-25x-45=0

a = 5; b = -25; c = -45;
Δ = b2-4ac
Δ = -252-4·5·(-45)
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{-(-25)-5\sqrt{61}}{2*5}=\frac{25-5\sqrt{61}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{61}}{2*5}=\frac{25+5\sqrt{61}}{10}
$