3/8x-9=2x+2

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

3/8x-9=2x+2

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-16x^2-88x+3=0

a = -16; b = -88; c = +3;
Δ = b2-4ac
Δ = -882-4·(-16)·3
Δ = 7936
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:

$\sqrt{\Delta}=\sqrt{7936}=\sqrt{256*31}=\sqrt{256}*\sqrt{31}=16\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-16\sqrt{31}}{2*-16}=\frac{88-16\sqrt{31}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+16\sqrt{31}}{2*-16}=\frac{88+16\sqrt{31}}{-32}
$