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x2-20x=-4
We move all terms to the left:
x2-20x-(-4)=0
We add all the numbers together, and all the variables
x^2-20x+4=0
a = 1; b = -20; c = +4;
Δ = b2-4ac
Δ = -202-4·1·4
Δ = 384
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{6}}{2*1}=\frac{20-8\sqrt{6}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{6}}{2*1}=\frac{20+8\sqrt{6}}{2} $
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