17x-9x(x+4)=3x-26

Solution for 17x-9x(x+4)=3x-26 equation:

17x-9x(x+4)=3x-26

We move all terms to the left:

17x-9x(x+4)-(3x-26)=0

We multiply parentheses

-9x^2+17x-36x-(3x-26)=0

We get rid of parentheses

-9x^2+17x-36x-3x+26=0

We add all the numbers together, and all the variables

-9x^2-22x+26=0

a = -9; b = -22; c = +26;
Δ = b2-4ac
Δ = -222-4·(-9)·26
Δ = 1420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{355}}{2*-9}=\frac{22-2\sqrt{355}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{355}}{2*-9}=\frac{22+2\sqrt{355}}{-18}
$