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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

4x(x-17)

We multiply parentheses

4x^2-68x

Back to the equation:

-(4x^2-68x)


We get rid of parentheses

2x^2-4x^2+2x+68x=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{-140}{-4}
=+35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-2}=\frac{0}{-4}
=0
$