4x(x-17)=x(2x+2)

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

4x(x-17)=x(2x+2)

We move all terms to the left:

4x(x-17)-(x(2x+2))=0

We multiply parentheses

4x^2-68x-(x(2x+2))=0


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

x(2x+2)

We multiply parentheses

2x^2+2x

Back to the equation:

-(2x^2+2x)


We get rid of parentheses

4x^2-2x^2-68x-2x=0

We add all the numbers together, and all the variables

2x^2-70x=0

a = 2; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·2·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*2}=\frac{140}{4}
=35
$