7x^2+13x-12=24-6x

Solution for 7x^2+13x-12=24-6x equation:

7x^2+13x-12=24-6x

We move all terms to the left:

7x^2+13x-12-(24-6x)=0

We add all the numbers together, and all the variables

7x^2+13x-(-6x+24)-12=0

We get rid of parentheses

7x^2+13x+6x-24-12=0

We add all the numbers together, and all the variables

7x^2+19x-36=0

a = 7; b = 19; c = -36;
Δ = b2-4ac
Δ = 192-4·7·(-36)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-37}{2*7}=\frac{-56}{14}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+37}{2*7}=\frac{18}{14}
=1+2/7
$