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-x^2+15x+31=0
We add all the numbers together, and all the variables
-1x^2+15x+31=0
a = -1; b = 15; c = +31;
Δ = b2-4ac
Δ = 152-4·(-1)·31
Δ = 349
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{349}}{2*-1}=\frac{-15-\sqrt{349}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{349}}{2*-1}=\frac{-15+\sqrt{349}}{-2} $
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