18x^2+12x+2=7

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

18x^2+12x+2=7

We move all terms to the left:

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

We add all the numbers together, and all the variables

18x^2+12x-5=0

a = 18; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·18·(-5)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{14}}{2*18}=\frac{-12-6\sqrt{14}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{14}}{2*18}=\frac{-12+6\sqrt{14}}{36}
$