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10x^2+15x-71=-3
We move all terms to the left:
10x^2+15x-71-(-3)=0
We add all the numbers together, and all the variables
10x^2+15x-68=0
a = 10; b = 15; c = -68;
Δ = b2-4ac
Δ = 152-4·10·(-68)
Δ = 2945
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{2945}}{2*10}=\frac{-15-\sqrt{2945}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{2945}}{2*10}=\frac{-15+\sqrt{2945}}{20} $
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