x2+13x=59

Solution for x2+13x=59 equation:

X2+13X=59

We move all terms to the left:

X2+13X-(59)=0

We add all the numbers together, and all the variables

X^2+13X-59=0

a = 1; b = 13; c = -59;
Δ = b2-4ac
Δ = 132-4·1·(-59)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-9\sqrt{5}}{2*1}=\frac{-13-9\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+9\sqrt{5}}{2*1}=\frac{-13+9\sqrt{5}}{2}
$