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3x^2-42x+87=0
a = 3; b = -42; c = +87;
Δ = b2-4ac
Δ = -422-4·3·87
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-12\sqrt{5}}{2*3}=\frac{42-12\sqrt{5}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+12\sqrt{5}}{2*3}=\frac{42+12\sqrt{5}}{6} $
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