X+9/5x=84

Solution for X+9/5x=84 equation:

X+9/5X=84

We move all terms to the left:

X+9/5X-(84)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-84*5X+9=0

Wy multiply elements

5X^2-420X+9=0

a = 5; b = -420; c = +9;
Δ = b2-4ac
Δ = -4202-4·5·9
Δ = 176220
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:

$\sqrt{\Delta}=\sqrt{176220}=\sqrt{36*4895}=\sqrt{36}*\sqrt{4895}=6\sqrt{4895}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-6\sqrt{4895}}{2*5}=\frac{420-6\sqrt{4895}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+6\sqrt{4895}}{2*5}=\frac{420+6\sqrt{4895}}{10}
$