12x+7x^2=12

Solution for 12x+7x^2=12 equation:

12x+7x^2=12

We move all terms to the left:

12x+7x^2-(12)=0

a = 7; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·7·(-12)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{30}}{2*7}=\frac{-12-4\sqrt{30}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{30}}{2*7}=\frac{-12+4\sqrt{30}}{14}
$