12x^2-3x=45

Solution for 12x^2-3x=45 equation:

12x^2-3x=45

We move all terms to the left:

12x^2-3x-(45)=0

a = 12; b = -3; c = -45;
Δ = b2-4ac
Δ = -32-4·12·(-45)
Δ = 2169
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:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{241}}{2*12}=\frac{3-3\sqrt{241}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{241}}{2*12}=\frac{3+3\sqrt{241}}{24}
$