30-1/26(3x)=20-1/26(2x)

Solution for 30-1/26(3x)=20-1/26(2x) equation:

30-1/26(3x)=20-1/26(2x)

We move all terms to the left:

30-1/26(3x)-(20-1/26(2x))=0


Domain of the equation: 263x!=0

x!=0/263

x!=0

x∈R



Domain of the equation: 262x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/263x-(-1/262x+20)+30=0

We get rid of parentheses

-1/263x+1/262x-20+30=0

We calculate fractions


(-262x)/68906x^2+263x/68906x^2-20+30=0

We add all the numbers together, and all the variables

(-262x)/68906x^2+263x/68906x^2+10=0

We multiply all the terms by the denominator


(-262x)+263x+10*68906x^2=0

We add all the numbers together, and all the variables

263x+(-262x)+10*68906x^2=0

Wy multiply elements

689060x^2+263x+(-262x)=0

We get rid of parentheses

689060x^2+263x-262x=0

We add all the numbers together, and all the variables

689060x^2+x=0

a = 689060; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·689060·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*689060}=\frac{-2}{1378120}
=-1/689060
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*689060}=\frac{0}{1378120}
=0
$