17x^2-19x-23=8x^2-5x

Solution for 17x^2-19x-23=8x^2-5x equation:

17x^2-19x-23=8x^2-5x

We move all terms to the left:

17x^2-19x-23-(8x^2-5x)=0

We get rid of parentheses

17x^2-8x^2-19x+5x-23=0

We add all the numbers together, and all the variables

9x^2-14x-23=0

a = 9; b = -14; c = -23;
Δ = b2-4ac
Δ = -142-4·9·(-23)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-32}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+32}{2*9}=\frac{46}{18}
=2+5/9
$