-4x^2+3+15x^2-4-12x=0

Solution for -4x^2+3+15x^2-4-12x=0 equation:

-4x^2+3+15x^2-4-12x=0

We add all the numbers together, and all the variables

11x^2-12x-1=0

a = 11; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·11·(-1)
Δ = 188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{47}}{2*11}=\frac{12-2\sqrt{47}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{47}}{2*11}=\frac{12+2\sqrt{47}}{22}
$