12x^2-x=24

Solution for 12x^2-x=24 equation:

12x^2-x=24

We move all terms to the left:

12x^2-x-(24)=0

We add all the numbers together, and all the variables

12x^2-1x-24=0

a = 12; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·12·(-24)
Δ = 1153
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{-(-1)-\sqrt{1153}}{2*12}=\frac{1-\sqrt{1153}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1153}}{2*12}=\frac{1+\sqrt{1153}}{24}
$