2=4x^2+3x-9

Solution for 2=4x^2+3x-9 equation:

2=4x^2+3x-9

We move all terms to the left:

2-(4x^2+3x-9)=0

We get rid of parentheses

-4x^2-3x+9+2=0

We add all the numbers together, and all the variables

-4x^2-3x+11=0

a = -4; b = -3; c = +11;
Δ = b2-4ac
Δ = -32-4·(-4)·11
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{185}}{2*-4}=\frac{3-\sqrt{185}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{185}}{2*-4}=\frac{3+\sqrt{185}}{-8}
$