12x^2+6x=5

Solution for 12x^2+6x=5 equation:

12x^2+6x=5

We move all terms to the left:

12x^2+6x-(5)=0

a = 12; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·12·(-5)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*12}=\frac{-6-2\sqrt{69}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*12}=\frac{-6+2\sqrt{69}}{24}
$