3x-22=4/5x

Solution for 3x-22=4/5x equation:

3x-22=4/5x

We move all terms to the left:

3x-22-(4/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+4/5x)-22=0

We get rid of parentheses

3x-4/5x-22=0

We multiply all the terms by the denominator


3x*5x-22*5x-4=0

Wy multiply elements

15x^2-110x-4=0

a = 15; b = -110; c = -4;
Δ = b2-4ac
Δ = -1102-4·15·(-4)
Δ = 12340
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:

$\sqrt{\Delta}=\sqrt{12340}=\sqrt{4*3085}=\sqrt{4}*\sqrt{3085}=2\sqrt{3085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3085}}{2*15}=\frac{110-2\sqrt{3085}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3085}}{2*15}=\frac{110+2\sqrt{3085}}{30}
$