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0=x^2-10x+19
We move all terms to the left:
0-(x^2-10x+19)=0
We add all the numbers together, and all the variables
-(x^2-10x+19)=0
We get rid of parentheses
-x^2+10x-19=0
We add all the numbers together, and all the variables
-1x^2+10x-19=0
a = -1; b = 10; c = -19;
Δ = b2-4ac
Δ = 102-4·(-1)·(-19)
Δ = 24
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{6}}{2*-1}=\frac{-10-2\sqrt{6}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{6}}{2*-1}=\frac{-10+2\sqrt{6}}{-2} $
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