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0=x^2+5x-69
We move all terms to the left:
0-(x^2+5x-69)=0
We add all the numbers together, and all the variables
-(x^2+5x-69)=0
We get rid of parentheses
-x^2-5x+69=0
We add all the numbers together, and all the variables
-1x^2-5x+69=0
a = -1; b = -5; c = +69;
Δ = b2-4ac
Δ = -52-4·(-1)·69
Δ = 301
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{301}}{2*-1}=\frac{5-\sqrt{301}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{301}}{2*-1}=\frac{5+\sqrt{301}}{-2} $
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