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4r+8=182/3*12r
We move all terms to the left:
4r+8-(182/3*12r)=0
Domain of the equation: 3*12r)!=0We add all the numbers together, and all the variables
r!=0/1
r!=0
r∈R
4r-(+182/3*12r)+8=0
We get rid of parentheses
4r-182/3*12r+8=0
We multiply all the terms by the denominator
4r*3*12r+8*3*12r-182=0
Wy multiply elements
144r^2*1+288r*1-182=0
Wy multiply elements
144r^2+288r-182=0
a = 144; b = 288; c = -182;
Δ = b2-4ac
Δ = 2882-4·144·(-182)
Δ = 187776
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}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{187776}=\sqrt{576*326}=\sqrt{576}*\sqrt{326}=24\sqrt{326}$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-24\sqrt{326}}{2*144}=\frac{-288-24\sqrt{326}}{288} $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+24\sqrt{326}}{2*144}=\frac{-288+24\sqrt{326}}{288} $
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