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-2(x-2)x-4x=3x+1-9x
We move all terms to the left:
-2(x-2)x-4x-(3x+1-9x)=0
We add all the numbers together, and all the variables
-2(x-2)x-4x-(-6x+1)=0
We add all the numbers together, and all the variables
-4x-2(x-2)x-(-6x+1)=0
We multiply parentheses
-2x^2-4x+4x-(-6x+1)=0
We get rid of parentheses
-2x^2-4x+4x+6x-1=0
We add all the numbers together, and all the variables
-2x^2+6x-1=0
a = -2; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-2)·(-1)
Δ = 28
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{7}}{2*-2}=\frac{-6-2\sqrt{7}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{7}}{2*-2}=\frac{-6+2\sqrt{7}}{-4} $
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