3x(8x+7)=2x(4+2x)

Solution for 3x(8x+7)=2x(4+2x) equation:

3x(8x+7)=2x(4+2x)

We move all terms to the left:

3x(8x+7)-(2x(4+2x))=0

We add all the numbers together, and all the variables

3x(8x+7)-(2x(2x+4))=0

We multiply parentheses

24x^2+21x-(2x(2x+4))=0


We calculate terms in parentheses: -(2x(2x+4)), so:

2x(2x+4)

We multiply parentheses

4x^2+8x

Back to the equation:

-(4x^2+8x)


We get rid of parentheses

24x^2-4x^2+21x-8x=0

We add all the numbers together, and all the variables

20x^2+13x=0

a = 20; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·20·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*20}=\frac{-26}{40}
=-13/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*20}=\frac{0}{40}
=0
$