4x2+3x-12=6x2-7x-60

Solution for 4x2+3x-12=6x2-7x-60 equation:

4x^2+3x-12=6x^2-7x-60

We move all terms to the left:

4x^2+3x-12-(6x^2-7x-60)=0

We get rid of parentheses

4x^2-6x^2+3x+7x+60-12=0

We add all the numbers together, and all the variables

-2x^2+10x+48=0

a = -2; b = 10; c = +48;
Δ = b2-4ac
Δ = 102-4·(-2)·48
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-22}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+22}{2*-2}=\frac{12}{-4}
=-3
$