x^2+26x=37

Solution for x^2+26x=37 equation:

x^2+26x=37

We move all terms to the left:

x^2+26x-(37)=0

a = 1; b = 26; c = -37;
Δ = b2-4ac
Δ = 262-4·1·(-37)
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{206}}{2*1}=\frac{-26-2\sqrt{206}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{206}}{2*1}=\frac{-26+2\sqrt{206}}{2}
$