8x+12x^2=1416

Solution for 8x+12x^2=1416 equation:

8x+12x^2=1416

We move all terms to the left:

8x+12x^2-(1416)=0

a = 12; b = 8; c = -1416;
Δ = b2-4ac
Δ = 82-4·12·(-1416)
Δ = 68032
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:

$\sqrt{\Delta}=\sqrt{68032}=\sqrt{64*1063}=\sqrt{64}*\sqrt{1063}=8\sqrt{1063}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{1063}}{2*12}=\frac{-8-8\sqrt{1063}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{1063}}{2*12}=\frac{-8+8\sqrt{1063}}{24}
$