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10k^2-97=3k+659
We move all terms to the left:
10k^2-97-(3k+659)=0
We get rid of parentheses
10k^2-3k-659-97=0
We add all the numbers together, and all the variables
10k^2-3k-756=0
a = 10; b = -3; c = -756;
Δ = b2-4ac
Δ = -32-4·10·(-756)
Δ = 30249
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{30249}=\sqrt{9*3361}=\sqrt{9}*\sqrt{3361}=3\sqrt{3361}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{3361}}{2*10}=\frac{3-3\sqrt{3361}}{20} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{3361}}{2*10}=\frac{3+3\sqrt{3361}}{20} $
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