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

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

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

We move all terms to the left:

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


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

2x(2x+3)

We multiply parentheses

4x^2+6x

Back to the equation:

-(4x^2+6x)


We get rid of parentheses

-4x^2+4x-6x+3=0

We add all the numbers together, and all the variables

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

a = -4; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-4)·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*-4}=\frac{2-2\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*-4}=\frac{2+2\sqrt{13}}{-8}
$