x+7(4-x)=3x+2(x-1)x

Solution for x+7(4-x)=3x+2(x-1)x equation:

x+7(4-x)=3x+2(x-1)x

We move all terms to the left:

x+7(4-x)-(3x+2(x-1)x)=0

We add all the numbers together, and all the variables

x+7(-1x+4)-(3x+2(x-1)x)=0

We multiply parentheses

x-7x-(3x+2(x-1)x)+28=0


We calculate terms in parentheses: -(3x+2(x-1)x), so:

3x+2(x-1)x

We multiply parentheses

2x^2+3x-2x

We add all the numbers together, and all the variables

2x^2+x

Back to the equation:

-(2x^2+x)


We add all the numbers together, and all the variables

-6x-(2x^2+x)+28=0

We get rid of parentheses

-2x^2-6x-x+28=0

We add all the numbers together, and all the variables

-2x^2-7x+28=0

a = -2; b = -7; c = +28;
Δ = b2-4ac
Δ = -72-4·(-2)·28
Δ = 273
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{273}}{2*-2}=\frac{7-\sqrt{273}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{273}}{2*-2}=\frac{7+\sqrt{273}}{-4}
$