45x^2=84x-12

Solution for 45x^2=84x-12 equation:

45x^2=84x-12

We move all terms to the left:

45x^2-(84x-12)=0

We get rid of parentheses

45x^2-84x+12=0

a = 45; b = -84; c = +12;
Δ = b2-4ac
Δ = -842-4·45·12
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{34}}{2*45}=\frac{84-12\sqrt{34}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{34}}{2*45}=\frac{84+12\sqrt{34}}{90}
$