2x(x+5)=24

Solution for 2x(x+5)=24 equation:

2x(x+5)=24

We move all terms to the left:

2x(x+5)-(24)=0

We multiply parentheses

2x^2+10x-24=0

a = 2; b = 10; c = -24;
Δ = b2-4ac
Δ = 102-4·2·(-24)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{73}}{2*2}=\frac{-10-2\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{73}}{2*2}=\frac{-10+2\sqrt{73}}{4}
$