8x^2+2=9x+2

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

8x^2+2=9x+2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-9x=0

a = 8; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·8·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*8}=\frac{18}{16}
=1+1/8
$