x(x+1)-56=4x(x-7)

Solution for x(x+1)-56=4x(x-7) equation:

x(x+1)-56=4x(x-7)

We move all terms to the left:

x(x+1)-56-(4x(x-7))=0

We multiply parentheses

x^2+x-(4x(x-7))-56=0


We calculate terms in parentheses: -(4x(x-7)), so:

4x(x-7)

We multiply parentheses

4x^2-28x

Back to the equation:

-(4x^2-28x)


We get rid of parentheses

x^2-4x^2+x+28x-56=0

We add all the numbers together, and all the variables

-3x^2+29x-56=0

a = -3; b = 29; c = -56;
Δ = b2-4ac
Δ = 292-4·(-3)·(-56)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-13}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+13}{2*-3}=\frac{-16}{-6}
=2+2/3
$