12x+12=1.5x^2

Solution for 12x+12=1.5x^2 equation:

12x+12=1.5x^2

We move all terms to the left:

12x+12-(1.5x^2)=0

We get rid of parentheses

-1.5x^2+12x+12=0

a = -1.5; b = 12; c = +12;
Δ = b2-4ac
Δ = 122-4·(-1.5)·12
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{6}}{2*-1.5}=\frac{-12-6\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{6}}{2*-1.5}=\frac{-12+6\sqrt{6}}{-3}
$