17=(4x^2)-3x+9

Solution for 17=(4x^2)-3x+9 equation:

17=(4x^2)-3x+9

We move all terms to the left:

17-((4x^2)-3x+9)=0

We get rid of parentheses

-4x^2+3x-9+17=0

We add all the numbers together, and all the variables

-4x^2+3x+8=0

a = -4; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-4)·8
Δ = 137
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{137}}{2*-4}=\frac{-3-\sqrt{137}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{137}}{2*-4}=\frac{-3+\sqrt{137}}{-8}
$