10^2=x(x+3x)

Solution for 10^2=x(x+3x) equation:

10^2=x(x+3x)

We move all terms to the left:

10^2-(x(x+3x))=0

We add all the numbers together, and all the variables

-(x(+4x))+10^2=0

We add all the numbers together, and all the variables

-(x(+4x))+100=0


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

x(+4x)

We multiply parentheses

4x^2

Back to the equation:

-(4x^2)


a = -4; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-4)·100
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*-4}=\frac{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*-4}=\frac{40}{-8}
=-5
$