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10x^2+20x-71=9
We move all terms to the left:
10x^2+20x-71-(9)=0
We add all the numbers together, and all the variables
10x^2+20x-80=0
a = 10; b = 20; c = -80;
Δ = b2-4ac
Δ = 202-4·10·(-80)
Δ = 3600
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{3600}=60$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-60}{2*10}=\frac{-80}{20} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+60}{2*10}=\frac{40}{20} =2 $
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