(8x-4)(17x-23)=(3x+17)

Solution for (8x-4)(17x-23)=(3x+17) equation:

(8x-4)(17x-23)=(3x+17)

We move all terms to the left:

(8x-4)(17x-23)-((3x+17))=0

We multiply parentheses ..

(+136x^2-184x-68x+92)-((3x+17))=0


We calculate terms in parentheses: -((3x+17)), so:

(3x+17)

We get rid of parentheses

3x+17

Back to the equation:

-(3x+17)


We get rid of parentheses

136x^2-184x-68x-3x+92-17=0

We add all the numbers together, and all the variables

136x^2-255x+75=0

a = 136; b = -255; c = +75;
Δ = b2-4ac
Δ = -2552-4·136·75
Δ = 24225
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:

$\sqrt{\Delta}=\sqrt{24225}=\sqrt{25*969}=\sqrt{25}*\sqrt{969}=5\sqrt{969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-255)-5\sqrt{969}}{2*136}=\frac{255-5\sqrt{969}}{272}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-255)+5\sqrt{969}}{2*136}=\frac{255+5\sqrt{969}}{272}
$