3x+5=2(2x+4)x=

Solution for 3x+5=2(2x+4)x= equation:

3x+5=2(2x+4)x=

We move all terms to the left:

3x+5-(2(2x+4)x)=0


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

2(2x+4)x

We multiply parentheses

4x^2+8x

Back to the equation:

-(4x^2+8x)


We get rid of parentheses

-4x^2+3x-8x+5=0

We add all the numbers together, and all the variables

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

a = -4; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-4)·5
Δ = 105
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{105}}{2*-4}=\frac{5-\sqrt{105}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*-4}=\frac{5+\sqrt{105}}{-8}
$