3x=-8.5-5/4x

Solution for 3x=-8.5-5/4x equation:

3x=-8.5-5/4x

We move all terms to the left:

3x-(-8.5-5/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-5/4x-8.5)=0

We get rid of parentheses

3x+5/4x+8.5=0

We multiply all the terms by the denominator


3x*4x+(8.5)*4x+5=0

We multiply parentheses

3x*4x+34x+5=0

Wy multiply elements

12x^2+34x+5=0

a = 12; b = 34; c = +5;
Δ = b2-4ac
Δ = 342-4·12·5
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{229}}{2*12}=\frac{-34-2\sqrt{229}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{229}}{2*12}=\frac{-34+2\sqrt{229}}{24}
$