6x^2+6x=1.5

Solution for 6x^2+6x=1.5 equation:

6x^2+6x=1.5

We move all terms to the left:

6x^2+6x-(1.5)=0

We add all the numbers together, and all the variables

6x^2+6x-1.5=0

a = 6; b = 6; c = -1.5;
Δ = b2-4ac
Δ = 62-4·6·(-1.5)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{2}}{2*6}=\frac{-6-6\sqrt{2}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{2}}{2*6}=\frac{-6+6\sqrt{2}}{12}
$