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3/2b+6+1/2b=15+3b
We move all terms to the left:
3/2b+6+1/2b-(15+3b)=0
Domain of the equation: 2b!=0We add all the numbers together, and all the variables
b!=0/2
b!=0
b∈R
3/2b+1/2b-(3b+15)+6=0
We get rid of parentheses
3/2b+1/2b-3b-15+6=0
We multiply all the terms by the denominator
-3b*2b-15*2b+6*2b+3+1=0
We add all the numbers together, and all the variables
-3b*2b-15*2b+6*2b+4=0
Wy multiply elements
-6b^2-30b+12b+4=0
We add all the numbers together, and all the variables
-6b^2-18b+4=0
a = -6; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·(-6)·4
Δ = 420
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}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*-6}=\frac{18-2\sqrt{105}}{-12} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*-6}=\frac{18+2\sqrt{105}}{-12} $
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