8x^2-9x=2^2-x

Solution for 8x^2-9x=2^2-x equation:

8x^2-9x=2^2-x

We move all terms to the left:

8x^2-9x-(2^2-x)=0

We get rid of parentheses

8x^2-9x+x-2^2=0

We add all the numbers together, and all the variables

8x^2-8x-4=0

a = 8; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·8·(-4)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{3}}{2*8}=\frac{8-8\sqrt{3}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{3}}{2*8}=\frac{8+8\sqrt{3}}{16}
$