16x(x+10)=x(x+10)

Solution for 16x(x+10)=x(x+10) equation:

16x(x+10)=x(x+10)

We move all terms to the left:

16x(x+10)-(x(x+10))=0

We multiply parentheses

16x^2+160x-(x(x+10))=0


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

x(x+10)

We multiply parentheses

x^2+10x

Back to the equation:

-(x^2+10x)


We get rid of parentheses

16x^2-x^2+160x-10x=0

We add all the numbers together, and all the variables

15x^2+150x=0

a = 15; b = 150; c = 0;
Δ = b2-4ac
Δ = 1502-4·15·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-150}{2*15}=\frac{-300}{30}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+150}{2*15}=\frac{0}{30}
=0
$