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x^2-22x=420
We move all terms to the left:
x^2-22x-(420)=0
a = 1; b = -22; c = -420;
Δ = b2-4ac
Δ = -222-4·1·(-420)
Δ = 2164
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{541}}{2*1}=\frac{22-2\sqrt{541}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{541}}{2*1}=\frac{22+2\sqrt{541}}{2} $
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