Y=10x-8/x=4

Solution for Y=10x-8/x=4 equation:

=10Y-8/Y=4

We move all terms to the left:

-(10Y-8/Y)=0


Domain of the equation: Y)!=0

Y!=0/1

Y!=0

Y∈R


We add all the numbers together, and all the variables

-(+10Y-8/Y)=0

We get rid of parentheses

-10Y+8/Y=0

We multiply all the terms by the denominator


-10Y*Y+8=0

Wy multiply elements

-10Y^2+8=0

a = -10; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-10)·8
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*-10}=\frac{0-8\sqrt{5}}{-20}
=-\frac{8\sqrt{5}}{-20}
=-\frac{2\sqrt{5}}{-5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*-10}=\frac{0+8\sqrt{5}}{-20}
=\frac{8\sqrt{5}}{-20}
=\frac{2\sqrt{5}}{-5}
$