4x^2-12x-34x^2-12x-3=0

Solution for 4x^2-12x-34x^2-12x-3=0 equation:

4x^2-12x-34x^2-12x-3=0

We add all the numbers together, and all the variables

-30x^2-24x-3=0

a = -30; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·(-30)·(-3)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{6}}{2*-30}=\frac{24-6\sqrt{6}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{6}}{2*-30}=\frac{24+6\sqrt{6}}{-60}
$