1/4*X=1/3*x-10

Solution for 1/4*X=1/3*x-10 equation:

1/4X=1/3X-10

We move all terms to the left:

1/4X-(1/3X-10)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R



Domain of the equation: 3X-10)!=0

X∈R


We get rid of parentheses

1/4X-1/3X+10=0

We calculate fractions


3X/12X^2+(-4X)/12X^2+10=0

We multiply all the terms by the denominator


3X+(-4X)+10*12X^2=0

Wy multiply elements

120X^2+3X+(-4X)=0

We get rid of parentheses

120X^2+3X-4X=0

We add all the numbers together, and all the variables

120X^2-1X=0

a = 120; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·120·0
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*120}=\frac{0}{240}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*120}=\frac{2}{240}
=1/120
$