(2x+3)-2x(x+3)=5x-2(1-x)x

Solution for (2x+3)-2x(x+3)=5x-2(1-x)x equation:

(2x+3)-2x(x+3)=5x-2(1-x)x

We move all terms to the left:

(2x+3)-2x(x+3)-(5x-2(1-x)x)=0

We add all the numbers together, and all the variables

(2x+3)-2x(x+3)-(5x-2(-1x+1)x)=0

We multiply parentheses

-2x^2+(2x+3)-6x-(5x-2(-1x+1)x)=0

We get rid of parentheses

-2x^2+2x-6x-(5x-2(-1x+1)x)+3=0


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

5x-2(-1x+1)x

We multiply parentheses

2x^2+5x-2x

We add all the numbers together, and all the variables

2x^2+3x

Back to the equation:

-(2x^2+3x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2-2x^2-4x-3x+3=0

We add all the numbers together, and all the variables

-4x^2-7x+3=0

a = -4; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·(-4)·3
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*-4}=\frac{7-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*-4}=\frac{7+\sqrt{97}}{-8}
$