12x-1/5x=4/5x+22

Solution for 12x-1/5x=4/5x+22 equation:

12x-1/5x=4/5x+22

We move all terms to the left:

12x-1/5x-(4/5x+22)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x+22)!=0

x∈R


We get rid of parentheses

12x-1/5x-4/5x-22=0

We multiply all the terms by the denominator


12x*5x-22*5x-1-4=0

We add all the numbers together, and all the variables

12x*5x-22*5x-5=0

Wy multiply elements

60x^2-110x-5=0

a = 60; b = -110; c = -5;
Δ = b2-4ac
Δ = -1102-4·60·(-5)
Δ = 13300
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:

$\sqrt{\Delta}=\sqrt{13300}=\sqrt{100*133}=\sqrt{100}*\sqrt{133}=10\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-10\sqrt{133}}{2*60}=\frac{110-10\sqrt{133}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+10\sqrt{133}}{2*60}=\frac{110+10\sqrt{133}}{120}
$