84x+105=12x^2-12x

Solution for 84x+105=12x^2-12x equation:

84x+105=12x^2-12x

We move all terms to the left:

84x+105-(12x^2-12x)=0

We get rid of parentheses

-12x^2+84x+12x+105=0

We add all the numbers together, and all the variables

-12x^2+96x+105=0

a = -12; b = 96; c = +105;
Δ = b2-4ac
Δ = 962-4·(-12)·105
Δ = 14256
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:

$\sqrt{\Delta}=\sqrt{14256}=\sqrt{1296*11}=\sqrt{1296}*\sqrt{11}=36\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-36\sqrt{11}}{2*-12}=\frac{-96-36\sqrt{11}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+36\sqrt{11}}{2*-12}=\frac{-96+36\sqrt{11}}{-24}
$