12x^2-16x+12=101

Solution for 12x^2-16x+12=101 equation:

12x^2-16x+12=101

We move all terms to the left:

12x^2-16x+12-(101)=0

We add all the numbers together, and all the variables

12x^2-16x-89=0

a = 12; b = -16; c = -89;
Δ = b2-4ac
Δ = -162-4·12·(-89)
Δ = 4528
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:

$\sqrt{\Delta}=\sqrt{4528}=\sqrt{16*283}=\sqrt{16}*\sqrt{283}=4\sqrt{283}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{283}}{2*12}=\frac{16-4\sqrt{283}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{283}}{2*12}=\frac{16+4\sqrt{283}}{24}
$