12x^2+12x+5=7

Solution for 12x^2+12x+5=7 equation:

12x^2+12x+5=7

We move all terms to the left:

12x^2+12x+5-(7)=0

We add all the numbers together, and all the variables

12x^2+12x-2=0

a = 12; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·12·(-2)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*12}=\frac{-12-4\sqrt{15}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*12}=\frac{-12+4\sqrt{15}}{24}
$