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5q+5q+1/2q=12
We move all terms to the left:
5q+5q+1/2q-(12)=0
Domain of the equation: 2q!=0We add all the numbers together, and all the variables
q!=0/2
q!=0
q∈R
10q+1/2q-12=0
We multiply all the terms by the denominator
10q*2q-12*2q+1=0
Wy multiply elements
20q^2-24q+1=0
a = 20; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·20·1
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{31}}{2*20}=\frac{24-4\sqrt{31}}{40} $$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{31}}{2*20}=\frac{24+4\sqrt{31}}{40} $
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