X^2+(4-3a)-12a=0

Solution for X^2+(4-3a)-12a=0 equation:

X^2+(4-3X)-12X=0

We add all the numbers together, and all the variables

X^2+(-3X+4)-12X=0

We add all the numbers together, and all the variables

X^2-12X+(-3X+4)=0

We get rid of parentheses

X^2-12X-3X+4=0

We add all the numbers together, and all the variables

X^2-15X+4=0

a = 1; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·1·4
Δ = 209
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{-(-15)-\sqrt{209}}{2*1}=\frac{15-\sqrt{209}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{209}}{2*1}=\frac{15+\sqrt{209}}{2}
$