39x-126=3x^2

Solution for 39x-126=3x^2 equation:

39x-126=3x^2

We move all terms to the left:

39x-126-(3x^2)=0

determiningTheFunctionDomain
-3x^2+39x-126=0

a = -3; b = 39; c = -126;
Δ = b2-4ac
Δ = 392-4·(-3)·(-126)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3}{2*-3}=\frac{-36}{-6}
=+6
$