9x^2+4x-17=x+3

Solution for 9x^2+4x-17=x+3 equation:

9x^2+4x-17=x+3

We move all terms to the left:

9x^2+4x-17-(x+3)=0

We get rid of parentheses

9x^2+4x-x-3-17=0

We add all the numbers together, and all the variables

9x^2+3x-20=0

a = 9; b = 3; c = -20;
Δ = b2-4ac
Δ = 32-4·9·(-20)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*9}=\frac{-30}{18}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*9}=\frac{24}{18}
=1+1/3
$