12x^2=0.75-4x

Solution for 12x^2=0.75-4x equation:

12x^2=0.75-4x

We move all terms to the left:

12x^2-(0.75-4x)=0

We add all the numbers together, and all the variables

12x^2-(-4x+0.75)=0

We get rid of parentheses

12x^2+4x-0.75=0

a = 12; b = 4; c = -0.75;
Δ = b2-4ac
Δ = 42-4·12·(-0.75)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{13}}{2*12}=\frac{-4-2\sqrt{13}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{13}}{2*12}=\frac{-4+2\sqrt{13}}{24}
$