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10k^2-97=3k^2+659
We move all terms to the left:
10k^2-97-(3k^2+659)=0
We get rid of parentheses
10k^2-3k^2-659-97=0
We add all the numbers together, and all the variables
7k^2-756=0
a = 7; b = 0; c = -756;
Δ = b2-4ac
Δ = 02-4·7·(-756)
Δ = 21168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21168}=\sqrt{7056*3}=\sqrt{7056}*\sqrt{3}=84\sqrt{3}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{3}}{2*7}=\frac{0-84\sqrt{3}}{14} =-\frac{84\sqrt{3}}{14} =-6\sqrt{3} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{3}}{2*7}=\frac{0+84\sqrt{3}}{14} =\frac{84\sqrt{3}}{14} =6\sqrt{3} $
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