6x(2x+6)=5x+20

Solution for 6x(2x+6)=5x+20 equation:

6x(2x+6)=5x+20

We move all terms to the left:

6x(2x+6)-(5x+20)=0

We multiply parentheses

12x^2+36x-(5x+20)=0

We get rid of parentheses

12x^2+36x-5x-20=0

We add all the numbers together, and all the variables

12x^2+31x-20=0

a = 12; b = 31; c = -20;
Δ = b2-4ac
Δ = 312-4·12·(-20)
Δ = 1921
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{-(31)-\sqrt{1921}}{2*12}=\frac{-31-\sqrt{1921}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1921}}{2*12}=\frac{-31+\sqrt{1921}}{24}
$