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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3(2x+2)-5x(x-2)), so:

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

We multiply parentheses

-5x^2+6x+10x+6

We add all the numbers together, and all the variables

-5x^2+16x+6

Back to the equation:

-(-5x^2+16x+6)


We get rid of parentheses

5x^2-16x+2x-6+3=0

We add all the numbers together, and all the variables

5x^2-14x-3=0

a = 5; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·5·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*5}=\frac{30}{10}
=3
$