12x^2+16x=100

Solution for 12x^2+16x=100 equation:

12x^2+16x=100

We move all terms to the left:

12x^2+16x-(100)=0

a = 12; b = 16; c = -100;
Δ = b2-4ac
Δ = 162-4·12·(-100)
Δ = 5056
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:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{79}}{2*12}=\frac{-16-8\sqrt{79}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{79}}{2*12}=\frac{-16+8\sqrt{79}}{24}
$