4(2/5)x=22

Solution for 4(2/5)x=22 equation:

4(2/5)x=22

We move all terms to the left:

4(2/5)x-(22)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(+2/5)x-22=0

We multiply parentheses

8x^2-22=0

a = 8; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·8·(-22)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*8}=\frac{0-8\sqrt{11}}{16}
=-\frac{8\sqrt{11}}{16}
=-\frac{\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*8}=\frac{0+8\sqrt{11}}{16}
=\frac{8\sqrt{11}}{16}
=\frac{\sqrt{11}}{2}
$