x(x+5)=61

Solution for x(x+5)=61 equation:

x(x+5)=61

We move all terms to the left:

x(x+5)-(61)=0

We multiply parentheses

x^2+5x-61=0

a = 1; b = 5; c = -61;
Δ = b2-4ac
Δ = 52-4·1·(-61)
Δ = 269
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{-(5)-\sqrt{269}}{2*1}=\frac{-5-\sqrt{269}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{269}}{2*1}=\frac{-5+\sqrt{269}}{2}
$