5x+21=4.95/x

Solution for 5x+21=4.95/x equation:

5x+21=4.95/x

We move all terms to the left:

5x+21-(4.95/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+4.95/x)+21=0

We get rid of parentheses

5x-4.95/x+21=0

We multiply all the terms by the denominator


5x*x+21*x-4.95=0

We add all the numbers together, and all the variables

21x+5x*x-4.95=0

Wy multiply elements

5x^2+21x-4.95=0

a = 5; b = 21; c = -4.95;
Δ = b2-4ac
Δ = 212-4·5·(-4.95)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-6\sqrt{15}}{2*5}=\frac{-21-6\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+6\sqrt{15}}{2*5}=\frac{-21+6\sqrt{15}}{10}
$