5x(x-2)+6x=30

Solution for 5x(x-2)+6x=30 equation:

5x(x-2)+6x=30

We move all terms to the left:

5x(x-2)+6x-(30)=0

We add all the numbers together, and all the variables

6x+5x(x-2)-30=0

We multiply parentheses

5x^2+6x-10x-30=0

We add all the numbers together, and all the variables

5x^2-4x-30=0

a = 5; b = -4; c = -30;
Δ = b2-4ac
Δ = -42-4·5·(-30)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{154}}{2*5}=\frac{4-2\sqrt{154}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{154}}{2*5}=\frac{4+2\sqrt{154}}{10}
$