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2j-61/2j=-12
We move all terms to the left:
2j-61/2j-(-12)=0
Domain of the equation: 2j!=0We add all the numbers together, and all the variables
j!=0/2
j!=0
j∈R
2j-61/2j+12=0
We multiply all the terms by the denominator
2j*2j+12*2j-61=0
Wy multiply elements
4j^2+24j-61=0
a = 4; b = 24; c = -61;
Δ = b2-4ac
Δ = 242-4·4·(-61)
Δ = 1552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{97}}{2*4}=\frac{-24-4\sqrt{97}}{8} $$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{97}}{2*4}=\frac{-24+4\sqrt{97}}{8} $
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