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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(7x(2x+4)), so:

7x(2x+4)

We multiply parentheses

14x^2+28x

Back to the equation:

-(14x^2+28x)


We get rid of parentheses

-14x^2+3x-28x+7=0

We add all the numbers together, and all the variables

-14x^2-25x+7=0

a = -14; b = -25; c = +7;
Δ = b2-4ac
Δ = -252-4·(-14)·7
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{113}}{2*-14}=\frac{25-3\sqrt{113}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{113}}{2*-14}=\frac{25+3\sqrt{113}}{-28}
$