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x*x-2x-3=50
We move all terms to the left:
x*x-2x-3-(50)=0
We add all the numbers together, and all the variables
-2x+x*x-53=0
Wy multiply elements
x^2-2x-53=0
a = 1; b = -2; c = -53;
Δ = b2-4ac
Δ = -22-4·1·(-53)
Δ = 216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{6}}{2*1}=\frac{2-6\sqrt{6}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{6}}{2*1}=\frac{2+6\sqrt{6}}{2} $
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