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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2+7x-1x-7)), so:

(+x^2+7x-1x-7)

We get rid of parentheses

x^2+7x-1x-7

We add all the numbers together, and all the variables

x^2+6x-7

Back to the equation:

-(x^2+6x-7)


We add all the numbers together, and all the variables

-4x-(x^2+6x-7)=0

We get rid of parentheses

-x^2-4x-6x+7=0

We add all the numbers together, and all the variables

-1x^2-10x+7=0

a = -1; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-1)·7
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{2}}{2*-1}=\frac{10-8\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{2}}{2*-1}=\frac{10+8\sqrt{2}}{-2}
$