x-3/5x+3=30

Solution for x-3/5x+3=30 equation:

x-3/5x+3=30

We move all terms to the left:

x-3/5x+3-(30)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x-3/5x-27=0

We multiply all the terms by the denominator


x*5x-27*5x-3=0

Wy multiply elements

5x^2-135x-3=0

a = 5; b = -135; c = -3;
Δ = b2-4ac
Δ = -1352-4·5·(-3)
Δ = 18285
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{-(-135)-\sqrt{18285}}{2*5}=\frac{135-\sqrt{18285}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18285}}{2*5}=\frac{135+\sqrt{18285}}{10}
$