-3(x-2)-4x2=0

Solution for -3(x-2)-4x2=0 equation:

-3(x-2)-4x^2=0

We multiply parentheses

-4x^2-3x+6=0

a = -4; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-4)·6
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{105}}{2*-4}=\frac{3-\sqrt{105}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*-4}=\frac{3+\sqrt{105}}{-8}
$