5x(2x-2)=3x(x+4)

Solution for 5x(2x-2)=3x(x+4) equation:

5x(2x-2)=3x(x+4)

We move all terms to the left:

5x(2x-2)-(3x(x+4))=0

We multiply parentheses

10x^2-10x-(3x(x+4))=0


We calculate terms in parentheses: -(3x(x+4)), so:

3x(x+4)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

10x^2-3x^2-10x-12x=0

We add all the numbers together, and all the variables

7x^2-22x=0

a = 7; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·7·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*7}=\frac{0}{14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*7}=\frac{44}{14}
=3+1/7
$