r-4/3r=10

Solution for r-4/3r=10 equation:

r-4/3r=10

We move all terms to the left:

r-4/3r-(10)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We multiply all the terms by the denominator


r*3r-10*3r-4=0

Wy multiply elements

3r^2-30r-4=0

a = 3; b = -30; c = -4;
Δ = b2-4ac
Δ = -302-4·3·(-4)
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{237}}{2*3}=\frac{30-2\sqrt{237}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{237}}{2*3}=\frac{30+2\sqrt{237}}{6}
$