(17/22)x=4/11

Solution for (17/22)x=4/11 equation:

(17/22)x=4/11

We move all terms to the left:

(17/22)x-(4/11)=0


Domain of the equation: 22)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+17/22)x-(+4/11)=0

We multiply parentheses

17x^2-(+4/11)=0

We get rid of parentheses

17x^2-4/11=0

We multiply all the terms by the denominator


17x^2*11-4=0

Wy multiply elements

187x^2-4=0

a = 187; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·187·(-4)
Δ = 2992
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:

$\sqrt{\Delta}=\sqrt{2992}=\sqrt{16*187}=\sqrt{16}*\sqrt{187}=4\sqrt{187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{187}}{2*187}=\frac{0-4\sqrt{187}}{374}
=-\frac{4\sqrt{187}}{374}
=-\frac{2\sqrt{187}}{187}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{187}}{2*187}=\frac{0+4\sqrt{187}}{374}
=\frac{4\sqrt{187}}{374}
=\frac{2\sqrt{187}}{187}
$