x(x-5)=59

Solution for x(x-5)=59 equation:

x(x-5)=59

We move all terms to the left:

x(x-5)-(59)=0

We multiply parentheses

x^2-5x-59=0

a = 1; b = -5; c = -59;
Δ = b2-4ac
Δ = -52-4·1·(-59)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{29}}{2*1}=\frac{5-3\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{29}}{2*1}=\frac{5+3\sqrt{29}}{2}
$