2x(5x+4)=6x(1+2x)

Solution for 2x(5x+4)=6x(1+2x) equation:

2x(5x+4)=6x(1+2x)

We move all terms to the left:

2x(5x+4)-(6x(1+2x))=0

We add all the numbers together, and all the variables

2x(5x+4)-(6x(2x+1))=0

We multiply parentheses

10x^2+8x-(6x(2x+1))=0


We calculate terms in parentheses: -(6x(2x+1)), so:

6x(2x+1)

We multiply parentheses

12x^2+6x

Back to the equation:

-(12x^2+6x)


We get rid of parentheses

10x^2-12x^2+8x-6x=0

We add all the numbers together, and all the variables

-2x^2+2x=0

a = -2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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