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(6x^2-4x+1)-(2x^2+6x-1)=1
We move all terms to the left:
(6x^2-4x+1)-(2x^2+6x-1)-(1)=0
We get rid of parentheses
6x^2-2x^2-4x-6x+1+1-1=0
We add all the numbers together, and all the variables
4x^2-10x+1=0
a = 4; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·4·1
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*4}=\frac{10-2\sqrt{21}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*4}=\frac{10+2\sqrt{21}}{8} $
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