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

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

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

We move all terms to the left:

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


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

2x(x+4)

We multiply parentheses

2x^2+8x

Back to the equation:

-(2x^2+8x)


We get rid of parentheses

-2x^2+3x-8x+4=0

We add all the numbers together, and all the variables

-2x^2-5x+4=0

a = -2; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-2)·4
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{57}}{2*-2}=\frac{5-\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*-2}=\frac{5+\sqrt{57}}{-4}
$