6x(x+5)=2x+18

Solution for 6x(x+5)=2x+18 equation:

6x(x+5)=2x+18

We move all terms to the left:

6x(x+5)-(2x+18)=0

We multiply parentheses

6x^2+30x-(2x+18)=0

We get rid of parentheses

6x^2+30x-2x-18=0

We add all the numbers together, and all the variables

6x^2+28x-18=0

a = 6; b = 28; c = -18;
Δ = b2-4ac
Δ = 282-4·6·(-18)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8\sqrt{19}}{2*6}=\frac{-28-8\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8\sqrt{19}}{2*6}=\frac{-28+8\sqrt{19}}{12}
$