3+5x=4(x+2)6x

Solution for 3+5x=4(x+2)6x equation:

3+5x=4(x+2)6x

We move all terms to the left:

3+5x-(4(x+2)6x)=0


We calculate terms in parentheses: -(4(x+2)6x), so:

4(x+2)6x

We multiply parentheses

24x^2+48x

Back to the equation:

-(24x^2+48x)


We get rid of parentheses

-24x^2+5x-48x+3=0

We add all the numbers together, and all the variables

-24x^2-43x+3=0

a = -24; b = -43; c = +3;
Δ = b2-4ac
Δ = -432-4·(-24)·3
Δ = 2137
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{-(-43)-\sqrt{2137}}{2*-24}=\frac{43-\sqrt{2137}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{2137}}{2*-24}=\frac{43+\sqrt{2137}}{-48}
$