5x(x+2)-3x(x+6)=40

Solution for 5x(x+2)-3x(x+6)=40 equation:

5x(x+2)-3x(x+6)=40

We move all terms to the left:

5x(x+2)-3x(x+6)-(40)=0

We multiply parentheses

5x^2-3x^2+10x-18x-40=0

We add all the numbers together, and all the variables

2x^2-8x-40=0

a = 2; b = -8; c = -40;
Δ = b2-4ac
Δ = -82-4·2·(-40)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{6}}{2*2}=\frac{8-8\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{6}}{2*2}=\frac{8+8\sqrt{6}}{4}
$