5x-4(x-3)=x(-x-7)

Solution for 5x-4(x-3)=x(-x-7) equation:

5x-4(x-3)=x(-x-7)

We move all terms to the left:

5x-4(x-3)-(x(-x-7))=0

We add all the numbers together, and all the variables

5x-4(x-3)-(x(-1x-7))=0

We multiply parentheses

5x-4x-(x(-1x-7))+12=0


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

x(-1x-7)

We multiply parentheses

-1x^2-7x

Back to the equation:

-(-1x^2-7x)


We add all the numbers together, and all the variables

-(-1x^2-7x)+x+12=0

We get rid of parentheses

1x^2+7x+x+12=0

We add all the numbers together, and all the variables

x^2+8x+12=0

a = 1; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·1·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*1}=\frac{-4}{2}
=-2
$