6x+36=4x^2

Solution for 6x+36=4x^2 equation:

6x+36=4x^2

We move all terms to the left:

6x+36-(4x^2)=0

determiningTheFunctionDomain
-4x^2+6x+36=0

a = -4; b = 6; c = +36;
Δ = b2-4ac
Δ = 62-4·(-4)·36
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{17}}{2*-4}=\frac{-6-6\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{17}}{2*-4}=\frac{-6+6\sqrt{17}}{-8}
$