8x^2=13-9x

Solution for 8x^2=13-9x equation:

8x^2=13-9x

We move all terms to the left:

8x^2-(13-9x)=0

We add all the numbers together, and all the variables

8x^2-(-9x+13)=0

We get rid of parentheses

8x^2+9x-13=0

a = 8; b = 9; c = -13;
Δ = b2-4ac
Δ = 92-4·8·(-13)
Δ = 497
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{-(9)-\sqrt{497}}{2*8}=\frac{-9-\sqrt{497}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{497}}{2*8}=\frac{-9+\sqrt{497}}{16}
$