2x(x+5)=82

Solution for 2x(x+5)=82 equation:

2x(x+5)=82

We move all terms to the left:

2x(x+5)-(82)=0

We multiply parentheses

2x^2+10x-82=0

a = 2; b = 10; c = -82;
Δ = b2-4ac
Δ = 102-4·2·(-82)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{21}}{2*2}=\frac{-10-6\sqrt{21}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{21}}{2*2}=\frac{-10+6\sqrt{21}}{4}
$