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36x^2-84x+37=0
a = 36; b = -84; c = +37;
Δ = b2-4ac
Δ = -842-4·36·37
Δ = 1728
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-24\sqrt{3}}{2*36}=\frac{84-24\sqrt{3}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+24\sqrt{3}}{2*36}=\frac{84+24\sqrt{3}}{72} $
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