12x^2+53x-24=-3+4x^2

Solution for 12x^2+53x-24=-3+4x^2 equation:

12x^2+53x-24=-3+4x^2

We move all terms to the left:

12x^2+53x-24-(-3+4x^2)=0

We get rid of parentheses

12x^2-4x^2+53x+3-24=0

We add all the numbers together, and all the variables

8x^2+53x-21=0

a = 8; b = 53; c = -21;
Δ = b2-4ac
Δ = 532-4·8·(-21)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-59}{2*8}=\frac{-112}{16}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+59}{2*8}=\frac{6}{16}
=3/8
$