4/10r-6/9r=4/7

Solution for 4/10r-6/9r=4/7 equation:

4/10r-6/9r=4/7

We move all terms to the left:

4/10r-6/9r-(4/7)=0


Domain of the equation: 10r!=0

r!=0/10

r!=0

r∈R



Domain of the equation: 9r!=0

r!=0/9

r!=0

r∈R


We add all the numbers together, and all the variables

4/10r-6/9r-(+4/7)=0

We get rid of parentheses

4/10r-6/9r-4/7=0

We calculate fractions


(-3240r^2)/4410r^2+1764r/4410r^2+(-2940r)/4410r^2=0

We multiply all the terms by the denominator


(-3240r^2)+1764r+(-2940r)=0

We get rid of parentheses

-3240r^2+1764r-2940r=0

We add all the numbers together, and all the variables

-3240r^2-1176r=0

a = -3240; b = -1176; c = 0;
Δ = b2-4ac
Δ = -11762-4·(-3240)·0
Δ = 1382976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1382976}=1176$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1176)-1176}{2*-3240}=\frac{0}{-6480}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1176)+1176}{2*-3240}=\frac{2352}{-6480}
=-49/135
$