x^2+4x=61

Solution for x^2+4x=61 equation:

x^2+4x=61

We move all terms to the left:

x^2+4x-(61)=0

a = 1; b = 4; c = -61;
Δ = b2-4ac
Δ = 42-4·1·(-61)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{65}}{2*1}=\frac{-4-2\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{65}}{2*1}=\frac{-4+2\sqrt{65}}{2}
$