12x^2+28x=15x^2-24x

Solution for 12x^2+28x=15x^2-24x equation:

12x^2+28x=15x^2-24x

We move all terms to the left:

12x^2+28x-(15x^2-24x)=0

We get rid of parentheses

12x^2-15x^2+28x+24x=0

We add all the numbers together, and all the variables

-3x^2+52x=0

a = -3; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-3)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-3}=\frac{-104}{-6}
=17+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-3}=\frac{0}{-6}
=0
$