12x=4x^2-7

Solution for 12x=4x^2-7 equation:

12x=4x^2-7

We move all terms to the left:

12x-(4x^2-7)=0

We get rid of parentheses

-4x^2+12x+7=0

a = -4; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·(-4)·7
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-16}{2*-4}=\frac{-28}{-8}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+16}{2*-4}=\frac{4}{-8}
=-1/2
$