18x2=12(x+12)

Solution for 18x2=12(x+12) equation:

18x^2=12(x+12)

We move all terms to the left:

18x^2-(12(x+12))=0


We calculate terms in parentheses: -(12(x+12)), so:

12(x+12)

We multiply parentheses

12x+144

Back to the equation:

-(12x+144)


We get rid of parentheses

18x^2-12x-144=0

a = 18; b = -12; c = -144;
Δ = b2-4ac
Δ = -122-4·18·(-144)
Δ = 10512
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:

$\sqrt{\Delta}=\sqrt{10512}=\sqrt{144*73}=\sqrt{144}*\sqrt{73}=12\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{73}}{2*18}=\frac{12-12\sqrt{73}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{73}}{2*18}=\frac{12+12\sqrt{73}}{36}
$