3x(x+22)=12x+30

Solution for 3x(x+22)=12x+30 equation:

3x(x+22)=12x+30

We move all terms to the left:

3x(x+22)-(12x+30)=0

We multiply parentheses

3x^2+66x-(12x+30)=0

We get rid of parentheses

3x^2+66x-12x-30=0

We add all the numbers together, and all the variables

3x^2+54x-30=0

a = 3; b = 54; c = -30;
Δ = b2-4ac
Δ = 542-4·3·(-30)
Δ = 3276
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:

$\sqrt{\Delta}=\sqrt{3276}=\sqrt{36*91}=\sqrt{36}*\sqrt{91}=6\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{91}}{2*3}=\frac{-54-6\sqrt{91}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{91}}{2*3}=\frac{-54+6\sqrt{91}}{6}
$