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3x^2-37x+78=0
a = 3; b = -37; c = +78;
Δ = b2-4ac
Δ = -372-4·3·78
Δ = 433
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{433}}{2*3}=\frac{37-\sqrt{433}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{433}}{2*3}=\frac{37+\sqrt{433}}{6} $
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