(8x-17)(5x+37)=(17x-4)

Solution for (8x-17)(5x+37)=(17x-4) equation:

(8x-17)(5x+37)=(17x-4)

We move all terms to the left:

(8x-17)(5x+37)-((17x-4))=0

We multiply parentheses ..

(+40x^2+296x-85x-629)-((17x-4))=0


We calculate terms in parentheses: -((17x-4)), so:

(17x-4)

We get rid of parentheses

17x-4

Back to the equation:

-(17x-4)


We get rid of parentheses

40x^2+296x-85x-17x-629+4=0

We add all the numbers together, and all the variables

40x^2+194x-625=0

a = 40; b = 194; c = -625;
Δ = b2-4ac
Δ = 1942-4·40·(-625)
Δ = 137636
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:

$\sqrt{\Delta}=\sqrt{137636}=\sqrt{4*34409}=\sqrt{4}*\sqrt{34409}=2\sqrt{34409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(194)-2\sqrt{34409}}{2*40}=\frac{-194-2\sqrt{34409}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(194)+2\sqrt{34409}}{2*40}=\frac{-194+2\sqrt{34409}}{80}
$