403/10x=33-71/2x

Solution for 403/10x=33-71/2x equation:

403/10x=33-71/2x

We move all terms to the left:

403/10x-(33-71/2x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

403/10x-(-71/2x+33)=0

We get rid of parentheses

403/10x+71/2x-33=0

We calculate fractions


806x/20x^2+710x/20x^2-33=0

We multiply all the terms by the denominator


806x+710x-33*20x^2=0

We add all the numbers together, and all the variables

1516x-33*20x^2=0

Wy multiply elements

-660x^2+1516x=0

a = -660; b = 1516; c = 0;
Δ = b2-4ac
Δ = 15162-4·(-660)·0
Δ = 2298256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2298256}=1516$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1516)-1516}{2*-660}=\frac{-3032}{-1320}
=2+49/165
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1516)+1516}{2*-660}=\frac{0}{-1320}
=0
$