33/2+3/5x=7/10x+15

Solution for 33/2+3/5x=7/10x+15 equation:

33/2+3/5x=7/10x+15

We move all terms to the left:

33/2+3/5x-(7/10x+15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+15)!=0

x∈R


We get rid of parentheses

3/5x-7/10x-15+33/2=0

We calculate fractions


1650x^2/200x^2+120x/200x^2+(-140x)/200x^2-15=0

We multiply all the terms by the denominator


1650x^2+120x+(-140x)-15*200x^2=0

Wy multiply elements

1650x^2-3000x^2+120x+(-140x)=0

We get rid of parentheses

1650x^2-3000x^2+120x-140x=0

We add all the numbers together, and all the variables

-1350x^2-20x=0

a = -1350; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-1350)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-1350}=\frac{0}{-2700}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-1350}=\frac{40}{-2700}
=-2/135
$