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x^2-25x+126=0
a = 1; b = -25; c = +126;
Δ = b2-4ac
Δ = -252-4·1·126
Δ = 121
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-11}{2*1}=\frac{14}{2} =7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11}{2*1}=\frac{36}{2} =18 $
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