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(9k+5)(7k-8)=
We move all terms to the left:
(9k+5)(7k-8)-()=0
We add all the numbers together, and all the variables
(9k+5)(7k-8)=0
We multiply parentheses ..
(+63k^2-72k+35k-40)=0
We get rid of parentheses
63k^2-72k+35k-40=0
We add all the numbers together, and all the variables
63k^2-37k-40=0
a = 63; b = -37; c = -40;
Δ = b2-4ac
Δ = -372-4·63·(-40)
Δ = 11449
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{11449}=107$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-107}{2*63}=\frac{-70}{126} =-5/9 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+107}{2*63}=\frac{144}{126} =1+1/7 $
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