8x^2-5x+6=17x-3

Solution for 8x^2-5x+6=17x-3 equation:

8x^2-5x+6=17x-3

We move all terms to the left:

8x^2-5x+6-(17x-3)=0

We get rid of parentheses

8x^2-5x-17x+3+6=0

We add all the numbers together, and all the variables

8x^2-22x+9=0

a = 8; b = -22; c = +9;
Δ = b2-4ac
Δ = -222-4·8·9
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-14}{2*8}=\frac{8}{16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+14}{2*8}=\frac{36}{16}
=2+1/4
$