2x+9=3/8x-2

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

2x+9=3/8x-2

We move all terms to the left:

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


Domain of the equation: 8x-2)!=0

x∈R


We get rid of parentheses

2x-3/8x+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}
$