12x^2=14x-4

Solution for 12x^2=14x-4 equation:

12x^2=14x-4

We move all terms to the left:

12x^2-(14x-4)=0

We get rid of parentheses

12x^2-14x+4=0

a = 12; b = -14; c = +4;
Δ = b2-4ac
Δ = -142-4·12·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2}{2*12}=\frac{12}{24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*12}=\frac{16}{24}
=2/3
$