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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+24x^2+136x-12x-68)-((17x-23))=0


We calculate terms in parentheses: -((17x-23)), so:

(17x-23)

We get rid of parentheses

17x-23

Back to the equation:

-(17x-23)


We get rid of parentheses

24x^2+136x-12x-17x-68+23=0

We add all the numbers together, and all the variables

24x^2+107x-45=0

a = 24; b = 107; c = -45;
Δ = b2-4ac
Δ = 1072-4·24·(-45)
Δ = 15769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(107)-\sqrt{15769}}{2*24}=\frac{-107-\sqrt{15769}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(107)+\sqrt{15769}}{2*24}=\frac{-107+\sqrt{15769}}{48}
$