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(31-x)xx=-3
We move all terms to the left:
(31-x)xx-(-3)=0
We add all the numbers together, and all the variables
(-1x+31)xx-(-3)=0
We add all the numbers together, and all the variables
(-1x+31)xx+3=0
We multiply parentheses
-1x^2+31x+3=0
a = -1; b = 31; c = +3;
Δ = b2-4ac
Δ = 312-4·(-1)·3
Δ = 973
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{-(31)-\sqrt{973}}{2*-1}=\frac{-31-\sqrt{973}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{973}}{2*-1}=\frac{-31+\sqrt{973}}{-2} $
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