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20x-x^2=2x+5
We move all terms to the left:
20x-x^2-(2x+5)=0
We add all the numbers together, and all the variables
-1x^2+20x-(2x+5)=0
We get rid of parentheses
-1x^2+20x-2x-5=0
We add all the numbers together, and all the variables
-1x^2+18x-5=0
a = -1; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·(-1)·(-5)
Δ = 304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{19}}{2*-1}=\frac{-18-4\sqrt{19}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{19}}{2*-1}=\frac{-18+4\sqrt{19}}{-2} $
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