x(2x+13)=62

Solution for x(2x+13)=62 equation:

x(2x+13)=62

We move all terms to the left:

x(2x+13)-(62)=0

We multiply parentheses

2x^2+13x-62=0

a = 2; b = 13; c = -62;
Δ = b2-4ac
Δ = 132-4·2·(-62)
Δ = 665
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{665}}{2*2}=\frac{-13-\sqrt{665}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{665}}{2*2}=\frac{-13+\sqrt{665}}{4}
$