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-x2+2x=6x-50
We move all terms to the left:
-x2+2x-(6x-50)=0
We add all the numbers together, and all the variables
-1x^2+2x-(6x-50)=0
We get rid of parentheses
-1x^2+2x-6x+50=0
We add all the numbers together, and all the variables
-1x^2-4x+50=0
a = -1; b = -4; c = +50;
Δ = b2-4ac
Δ = -42-4·(-1)·50
Δ = 216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{6}}{2*-1}=\frac{4-6\sqrt{6}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{6}}{2*-1}=\frac{4+6\sqrt{6}}{-2} $
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