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

Solution for 5-(x+7)+4x=7x(x-1) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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


We calculate terms in parentheses: -(7x(x-1)), so:

7x(x-1)

We multiply parentheses

7x^2-7x

Back to the equation:

-(7x^2-7x)


We add all the numbers together, and all the variables

3x-(7x^2-7x)-2=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -7; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·(-7)·(-2)
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{11}}{2*-7}=\frac{-10-2\sqrt{11}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{11}}{2*-7}=\frac{-10+2\sqrt{11}}{-14}
$