-4x2+3=15x2-4-12x

Solution for -4x2+3=15x2-4-12x equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-19x^2+12x+7=0

a = -19; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·(-19)·7
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-26}{2*-19}=\frac{-38}{-38}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+26}{2*-19}=\frac{14}{-38}
=-7/19
$