12x^2=13x-3

Solution for 12x^2=13x-3 equation:

12x^2=13x-3

We move all terms to the left:

12x^2-(13x-3)=0

We get rid of parentheses

12x^2-13x+3=0

a = 12; b = -13; c = +3;
Δ = b2-4ac
Δ = -132-4·12·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*12}=\frac{8}{24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*12}=\frac{18}{24}
=3/4
$