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6B-30-1B=5(B-6)6B-6-1B=5(B-6)6B-30=5(B-6)
We move all terms to the left:
6B-30-1B-(5(B-6)6B-6-1B)=0
We add all the numbers together, and all the variables
5B-(5(B-6)6B-6-1B)-30=0
We calculate terms in parentheses: -(5(B-6)6B-6-1B), so:We get rid of parentheses
5(B-6)6B-6-1B
determiningTheFunctionDomain 5(B-6)6B-1B-6
We add all the numbers together, and all the variables
-1B+5(B-6)6B-6
We multiply parentheses
30B^2-1B-180B-6
We add all the numbers together, and all the variables
30B^2-181B-6
Back to the equation:
-(30B^2-181B-6)
-30B^2+5B+181B+6-30=0
We add all the numbers together, and all the variables
-30B^2+186B-24=0
a = -30; b = 186; c = -24;
Δ = b2-4ac
Δ = 1862-4·(-30)·(-24)
Δ = 31716
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31716}=\sqrt{36*881}=\sqrt{36}*\sqrt{881}=6\sqrt{881}$$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(186)-6\sqrt{881}}{2*-30}=\frac{-186-6\sqrt{881}}{-60} $$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(186)+6\sqrt{881}}{2*-30}=\frac{-186+6\sqrt{881}}{-60} $
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