2x(4x+7)=3x(2+3x)

Solution for 2x(4x+7)=3x(2+3x) equation:

2x(4x+7)=3x(2+3x)

We move all terms to the left:

2x(4x+7)-(3x(2+3x))=0

We add all the numbers together, and all the variables

2x(4x+7)-(3x(3x+2))=0

We multiply parentheses

8x^2+14x-(3x(3x+2))=0


We calculate terms in parentheses: -(3x(3x+2)), so:

3x(3x+2)

We multiply parentheses

9x^2+6x

Back to the equation:

-(9x^2+6x)


We get rid of parentheses

8x^2-9x^2+14x-6x=0

We add all the numbers together, and all the variables

-1x^2+8x=0

a = -1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-1)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-1}=\frac{0}{-2}
=0
$