9x+6-4x2=8

Solution for 9x+6-4x2=8 equation:

9x+6-4x^2=8

We move all terms to the left:

9x+6-4x^2-(8)=0

We add all the numbers together, and all the variables

-4x^2+9x-2=0

a = -4; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-4)·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*-4}=\frac{-2}{-8}
=1/4
$