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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

7(4x-7)

We multiply parentheses

28x-49

Back to the equation:

-(28x-49)


We get rid of parentheses

x^2+4x-28x+49=0

We add all the numbers together, and all the variables

x^2-24x+49=0

a = 1; b = -24; c = +49;
Δ = b2-4ac
Δ = -242-4·1·49
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{95}}{2*1}=\frac{24-2\sqrt{95}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{95}}{2*1}=\frac{24+2\sqrt{95}}{2}
$