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-x2=5x+1-16
We move all terms to the left:
-x2-(5x+1-16)=0
We add all the numbers together, and all the variables
-x2-(5x-15)=0
We add all the numbers together, and all the variables
-1x^2-(5x-15)=0
We get rid of parentheses
-1x^2-5x+15=0
a = -1; b = -5; c = +15;
Δ = b2-4ac
Δ = -52-4·(-1)·15
Δ = 85
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{-(-5)-\sqrt{85}}{2*-1}=\frac{5-\sqrt{85}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*-1}=\frac{5+\sqrt{85}}{-2} $
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