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0=x^2-5x-3
We move all terms to the left:
0-(x^2-5x-3)=0
We add all the numbers together, and all the variables
-(x^2-5x-3)=0
We get rid of parentheses
-x^2+5x+3=0
We add all the numbers together, and all the variables
-1x^2+5x+3=0
a = -1; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-1)·3
Δ = 37
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{37}}{2*-1}=\frac{-5-\sqrt{37}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-1}=\frac{-5+\sqrt{37}}{-2} $
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