12x+7=3x^2

Solution for 12x+7=3x^2 equation:

12x+7=3x^2

We move all terms to the left:

12x+7-(3x^2)=0

determiningTheFunctionDomain
-3x^2+12x+7=0

a = -3; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·(-3)·7
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{57}}{2*-3}=\frac{-12-2\sqrt{57}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{57}}{2*-3}=\frac{-12+2\sqrt{57}}{-6}
$