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10x^2+31x+15=0
a = 10; b = 31; c = +15;
Δ = b2-4ac
Δ = 312-4·10·15
Δ = 361
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-19}{2*10}=\frac{-50}{20} =-2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+19}{2*10}=\frac{-12}{20} =-3/5 $
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