r-4/3r=10

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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} $

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