2/3q-4=1/5q+10

Solution for 2/3q-4=1/5q+10 equation:

2/3q-4=1/5q+10

We move all terms to the left:

2/3q-4-(1/5q+10)=0


Domain of the equation: 3q!=0

q!=0/3

q!=0

q∈R



Domain of the equation: 5q+10)!=0

q∈R


We get rid of parentheses

2/3q-1/5q-10-4=0

We calculate fractions


10q/15q^2+(-3q)/15q^2-10-4=0

We add all the numbers together, and all the variables

10q/15q^2+(-3q)/15q^2-14=0

We multiply all the terms by the denominator


10q+(-3q)-14*15q^2=0

Wy multiply elements

-210q^2+10q+(-3q)=0

We get rid of parentheses

-210q^2+10q-3q=0

We add all the numbers together, and all the variables

-210q^2+7q=0

a = -210; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-210)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-210}=\frac{-14}{-420}
=1/30
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-210}=\frac{0}{-420}
=0
$