x2+13x=7

Solution for x2+13x=7 equation:

x2+13x=7

We move all terms to the left:

x2+13x-(7)=0

We add all the numbers together, and all the variables

x^2+13x-7=0

a = 1; b = 13; c = -7;
Δ = b2-4ac
Δ = 132-4·1·(-7)
Δ = 197
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{197}}{2*1}=\frac{-13-\sqrt{197}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{197}}{2*1}=\frac{-13+\sqrt{197}}{2}
$