7x^2-3=12x

Solution for 7x^2-3=12x equation:

7x^2-3=12x

We move all terms to the left:

7x^2-3-(12x)=0

a = 7; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·7·(-3)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{57}}{2*7}=\frac{12-2\sqrt{57}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{57}}{2*7}=\frac{12+2\sqrt{57}}{14}
$