5x(x+2x)=5(x+10)

Solution for 5x(x+2x)=5(x+10) equation:

5x(x+2x)=5(x+10)

We move all terms to the left:

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

We add all the numbers together, and all the variables

5x(+3x)-(5(x+10))=0

We multiply parentheses

15x^2-(5(x+10))=0


We calculate terms in parentheses: -(5(x+10)), so:

5(x+10)

We multiply parentheses

5x+50

Back to the equation:

-(5x+50)


We get rid of parentheses

15x^2-5x-50=0

a = 15; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·15·(-50)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-55}{2*15}=\frac{-50}{30}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+55}{2*15}=\frac{60}{30}
=2
$