8(x-3)+7=2x(4x-17)

Solution for 8(x-3)+7=2x(4x-17) equation:

8(x-3)+7=2x(4x-17)

We move all terms to the left:

8(x-3)+7-(2x(4x-17))=0

We multiply parentheses

8x-(2x(4x-17))-24+7=0


We calculate terms in parentheses: -(2x(4x-17)), so:

2x(4x-17)

We multiply parentheses

8x^2-34x

Back to the equation:

-(8x^2-34x)


We add all the numbers together, and all the variables

8x-(8x^2-34x)-17=0

We get rid of parentheses

-8x^2+8x+34x-17=0

We add all the numbers together, and all the variables

-8x^2+42x-17=0

a = -8; b = 42; c = -17;
Δ = b2-4ac
Δ = 422-4·(-8)·(-17)
Δ = 1220
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:

$\sqrt{\Delta}=\sqrt{1220}=\sqrt{4*305}=\sqrt{4}*\sqrt{305}=2\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{305}}{2*-8}=\frac{-42-2\sqrt{305}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{305}}{2*-8}=\frac{-42+2\sqrt{305}}{-16}
$