5(9)=x(x+x)

Solution for 5(9)=x(x+x) equation:

5(9)=x(x+x)

We move all terms to the left:

5(9)-(x(x+x))=0

We add all the numbers together, and all the variables

-(x(+2x))+59=0


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

x(+2x)

We multiply parentheses

2x^2

Back to the equation:

-(2x^2)


a = -2; b = 0; c = +59;
Δ = b2-4ac
Δ = 02-4·(-2)·59
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{118}}{2*-2}=\frac{0-2\sqrt{118}}{-4}
=-\frac{2\sqrt{118}}{-4}
=-\frac{\sqrt{118}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{118}}{2*-2}=\frac{0+2\sqrt{118}}{-4}
=\frac{2\sqrt{118}}{-4}
=\frac{\sqrt{118}}{-2}
$