5x(x-13)=200

Solution for 5x(x-13)=200 equation:

5x(x-13)=200

We move all terms to the left:

5x(x-13)-(200)=0

We multiply parentheses

5x^2-65x-200=0

a = 5; b = -65; c = -200;
Δ = b2-4ac
Δ = -652-4·5·(-200)
Δ = 8225
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:

$\sqrt{\Delta}=\sqrt{8225}=\sqrt{25*329}=\sqrt{25}*\sqrt{329}=5\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{329}}{2*5}=\frac{65-5\sqrt{329}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{329}}{2*5}=\frac{65+5\sqrt{329}}{10}
$