4x+32=6x^2+4

Solution for 4x+32=6x^2+4 equation:

4x+32=6x^2+4

We move all terms to the left:

4x+32-(6x^2+4)=0

We get rid of parentheses

-6x^2+4x-4+32=0

We add all the numbers together, and all the variables

-6x^2+4x+28=0

a = -6; b = 4; c = +28;
Δ = b2-4ac
Δ = 42-4·(-6)·28
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{43}}{2*-6}=\frac{-4-4\sqrt{43}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{43}}{2*-6}=\frac{-4+4\sqrt{43}}{-12}
$