7r-2/3r=0

Solution for 7r-2/3r=0 equation:

7r-2/3r=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We multiply all the terms by the denominator


7r*3r-2=0

Wy multiply elements

21r^2-2=0

a = 21; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·21·(-2)
Δ = 168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*21}=\frac{0-2\sqrt{42}}{42}
=-\frac{2\sqrt{42}}{42}
=-\frac{\sqrt{42}}{21}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*21}=\frac{0+2\sqrt{42}}{42}
=\frac{2\sqrt{42}}{42}
=\frac{\sqrt{42}}{21}
$