45x-(4/x)=8

Solution for 45x-(4/x)=8 equation:

45x-(4/x)=8

We move all terms to the left:

45x-(4/x)-(8)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

45x-(+4/x)-8=0

We get rid of parentheses

45x-4/x-8=0

We multiply all the terms by the denominator


45x*x-8*x-4=0

We add all the numbers together, and all the variables

-8x+45x*x-4=0

Wy multiply elements

45x^2-8x-4=0

a = 45; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·45·(-4)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*45}=\frac{-20}{90}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*45}=\frac{36}{90}
=2/5
$