X+30+2/5x+3/5x=360

Solution for X+30+2/5x+3/5x=360 equation:

X+30+2/5X+3/5X=360

We move all terms to the left:

X+30+2/5X+3/5X-(360)=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+2/5X+3/5X-330=0

We multiply all the terms by the denominator


X*5X-330*5X+2+3=0

We add all the numbers together, and all the variables

X*5X-330*5X+5=0

Wy multiply elements

5X^2-1650X+5=0

a = 5; b = -1650; c = +5;
Δ = b2-4ac
Δ = -16502-4·5·5
Δ = 2722400
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:

$\sqrt{\Delta}=\sqrt{2722400}=\sqrt{400*6806}=\sqrt{400}*\sqrt{6806}=20\sqrt{6806}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1650)-20\sqrt{6806}}{2*5}=\frac{1650-20\sqrt{6806}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1650)+20\sqrt{6806}}{2*5}=\frac{1650+20\sqrt{6806}}{10}
$