x(x+4x)=7(7+x+3)

Solution for x(x+4x)=7(7+x+3) equation:

x(x+4x)=7(7+x+3)

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(+5x)-(7(x+10))=0

We multiply parentheses

5x^2-(7(x+10))=0


We calculate terms in parentheses: -(7(x+10)), so:

7(x+10)

We multiply parentheses

7x+70

Back to the equation:

-(7x+70)


We get rid of parentheses

5x^2-7x-70=0

a = 5; b = -7; c = -70;
Δ = b2-4ac
Δ = -72-4·5·(-70)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{161}}{2*5}=\frac{7-3\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{161}}{2*5}=\frac{7+3\sqrt{161}}{10}
$