13x-12x+3x^2-12=13-12x

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

13x-12x+3x^2-12=13-12x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

3x^2+x+12x-13-12=0

We add all the numbers together, and all the variables

3x^2+13x-25=0

a = 3; b = 13; c = -25;
Δ = b2-4ac
Δ = 132-4·3·(-25)
Δ = 469
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{469}}{2*3}=\frac{-13-\sqrt{469}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{469}}{2*3}=\frac{-13+\sqrt{469}}{6}
$