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5x^2+15x+6=0
a = 5; b = 15; c = +6;
Δ = b2-4ac
Δ = 152-4·5·6
Δ = 105
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{-(15)-\sqrt{105}}{2*5}=\frac{-15-\sqrt{105}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{105}}{2*5}=\frac{-15+\sqrt{105}}{10} $
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