1/2x-10/3x=-17/4

Solution for 1/2x-10/3x=-17/4 equation:

1/2x-10/3x=-17/4

We move all terms to the left:

1/2x-10/3x-(-17/4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/2x-10/3x+17/4=0

We calculate fractions


306x^2/96x^2+48x/96x^2+(-320x)/96x^2=0

We multiply all the terms by the denominator


306x^2+48x+(-320x)=0

We get rid of parentheses

306x^2+48x-320x=0

We add all the numbers together, and all the variables

306x^2-272x=0

a = 306; b = -272; c = 0;
Δ = b2-4ac
Δ = -2722-4·306·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-272}{2*306}=\frac{0}{612}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+272}{2*306}=\frac{544}{612}
=8/9
$