2/5*x=22

Solution for 2/5*x=22 equation:

2/5*x=22

We move all terms to the left:

2/5*x-(22)=0


Domain of the equation: 5*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-22*5*x+2=0

Wy multiply elements

-110x*x+2=0

Wy multiply elements

-110x^2+2=0

a = -110; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-110)·2
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{55}}{2*-110}=\frac{0-4\sqrt{55}}{-220}
=-\frac{4\sqrt{55}}{-220}
=-\frac{\sqrt{55}}{-55}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{55}}{2*-110}=\frac{0+4\sqrt{55}}{-220}
=\frac{4\sqrt{55}}{-220}
=\frac{\sqrt{55}}{-55}
$