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22x^2-126x+169=0
a = 22; b = -126; c = +169;
Δ = b2-4ac
Δ = -1262-4·22·169
Δ = 1004
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1004}=\sqrt{4*251}=\sqrt{4}*\sqrt{251}=2\sqrt{251}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{251}}{2*22}=\frac{126-2\sqrt{251}}{44} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{251}}{2*22}=\frac{126+2\sqrt{251}}{44} $
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