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21x^2-5x-16=13
We move all terms to the left:
21x^2-5x-16-(13)=0
We add all the numbers together, and all the variables
21x^2-5x-29=0
a = 21; b = -5; c = -29;
Δ = b2-4ac
Δ = -52-4·21·(-29)
Δ = 2461
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{2461}}{2*21}=\frac{5-\sqrt{2461}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2461}}{2*21}=\frac{5+\sqrt{2461}}{42} $
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