5x^2=12x+6

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

5x^2=12x+6

We move all terms to the left:

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

We get rid of parentheses

5x^2-12x-6=0

a = 5; b = -12; c = -6;
Δ = b2-4ac
Δ = -122-4·5·(-6)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*5}=\frac{12-2\sqrt{66}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*5}=\frac{12+2\sqrt{66}}{10}
$