6x^2+18x+12=7

Solution for 6x^2+18x+12=7 equation:

6x^2+18x+12=7

We move all terms to the left:

6x^2+18x+12-(7)=0

We add all the numbers together, and all the variables

6x^2+18x+5=0

a = 6; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·6·5
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{51}}{2*6}=\frac{-18-2\sqrt{51}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{51}}{2*6}=\frac{-18+2\sqrt{51}}{12}
$