2x(x+2)-7=4x-5(2-x)

Solution for 2x(x+2)-7=4x-5(2-x) equation:

2x(x+2)-7=4x-5(2-x)

We move all terms to the left:

2x(x+2)-7-(4x-5(2-x))=0

We add all the numbers together, and all the variables

2x(x+2)-(4x-5(-1x+2))-7=0

We multiply parentheses

2x^2+4x-(4x-5(-1x+2))-7=0


We calculate terms in parentheses: -(4x-5(-1x+2)), so:

4x-5(-1x+2)

We multiply parentheses

4x+5x-10

We add all the numbers together, and all the variables

9x-10

Back to the equation:

-(9x-10)


We get rid of parentheses

2x^2+4x-9x+10-7=0

We add all the numbers together, and all the variables

2x^2-5x+3=0

a = 2; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·2·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*2}=\frac{6}{4}
=1+1/2
$