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5/6w+21=-2w+9/3
We move all terms to the left:
5/6w+21-(-2w+9/3)=0
Domain of the equation: 6w!=0We add all the numbers together, and all the variables
w!=0/6
w!=0
w∈R
5/6w-(-2w+3)+21=0
We get rid of parentheses
5/6w+2w-3+21=0
We multiply all the terms by the denominator
2w*6w-3*6w+21*6w+5=0
Wy multiply elements
12w^2-18w+126w+5=0
We add all the numbers together, and all the variables
12w^2+108w+5=0
a = 12; b = 108; c = +5;
Δ = b2-4ac
Δ = 1082-4·12·5
Δ = 11424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11424}=\sqrt{16*714}=\sqrt{16}*\sqrt{714}=4\sqrt{714}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{714}}{2*12}=\frac{-108-4\sqrt{714}}{24} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{714}}{2*12}=\frac{-108+4\sqrt{714}}{24} $
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