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s2-66s+135=0
We add all the numbers together, and all the variables
s^2-66s+135=0
a = 1; b = -66; c = +135;
Δ = b2-4ac
Δ = -662-4·1·135
Δ = 3816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3816}=\sqrt{36*106}=\sqrt{36}*\sqrt{106}=6\sqrt{106}$$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{106}}{2*1}=\frac{66-6\sqrt{106}}{2} $$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{106}}{2*1}=\frac{66+6\sqrt{106}}{2} $
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