5/8x+2=3x-9

Solution for 5/8x+2=3x-9 equation:

5/8x+2=3x-9

We move all terms to the left:

5/8x+2-(3x-9)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

5/8x-3x+9+2=0

We multiply all the terms by the denominator


-3x*8x+9*8x+2*8x+5=0

Wy multiply elements

-24x^2+72x+16x+5=0

We add all the numbers together, and all the variables

-24x^2+88x+5=0

a = -24; b = 88; c = +5;
Δ = b2-4ac
Δ = 882-4·(-24)·5
Δ = 8224
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:

$\sqrt{\Delta}=\sqrt{8224}=\sqrt{16*514}=\sqrt{16}*\sqrt{514}=4\sqrt{514}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-4\sqrt{514}}{2*-24}=\frac{-88-4\sqrt{514}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+4\sqrt{514}}{2*-24}=\frac{-88+4\sqrt{514}}{-48}
$