x(5x+3)=2x

Solution for x(5x+3)=2x equation:

x(5x+3)=2x

We move all terms to the left:

x(5x+3)-(2x)=0

We add all the numbers together, and all the variables

-2x+x(5x+3)=0

We multiply parentheses

5x^2-2x+3x=0

We add all the numbers together, and all the variables

5x^2+x=0

a = 5; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·5·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*5}=\frac{0}{10}
=0
$