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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

9x-(x+7)-(7x(x-1))=0

We get rid of parentheses

9x-x-(7x(x-1))-7=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

8x-(7x^2-7x)-7=0

We get rid of parentheses

-7x^2+8x+7x-7=0

We add all the numbers together, and all the variables

-7x^2+15x-7=0

a = -7; b = 15; c = -7;
Δ = b2-4ac
Δ = 152-4·(-7)·(-7)
Δ = 29
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{-(15)-\sqrt{29}}{2*-7}=\frac{-15-\sqrt{29}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{29}}{2*-7}=\frac{-15+\sqrt{29}}{-14}
$