3/8x+2=3x+9

Solution for 3/8x+2=3x+9 equation:

3/8x+2=3x+9

We move all terms to the left:

3/8x+2-(3x+9)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

3/8x-3x-9+2=0

We multiply all the terms by the denominator


-3x*8x-9*8x+2*8x+3=0

Wy multiply elements

-24x^2-72x+16x+3=0

We add all the numbers together, and all the variables

-24x^2-56x+3=0

a = -24; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·(-24)·3
Δ = 3424
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:

$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{214}}{2*-24}=\frac{56-4\sqrt{214}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{214}}{2*-24}=\frac{56+4\sqrt{214}}{-48}
$