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42=x2-6x+2
We move all terms to the left:
42-(x2-6x+2)=0
We add all the numbers together, and all the variables
-(+x^2-6x+2)+42=0
We get rid of parentheses
-x^2+6x-2+42=0
We add all the numbers together, and all the variables
-1x^2+6x+40=0
a = -1; b = 6; c = +40;
Δ = b2-4ac
Δ = 62-4·(-1)·40
Δ = 196
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-1}=\frac{-20}{-2} =+10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-1}=\frac{8}{-2} =-4 $
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