X+3/5x=9

Solution for X+3/5x=9 equation:

X+3/5X=9

We move all terms to the left:

X+3/5X-(9)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-9*5X+3=0

Wy multiply elements

5X^2-45X+3=0

a = 5; b = -45; c = +3;
Δ = b2-4ac
Δ = -452-4·5·3
Δ = 1965
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1965}}{2*5}=\frac{45-\sqrt{1965}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1965}}{2*5}=\frac{45+\sqrt{1965}}{10}
$