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-2x(3x-1)=-6x-1
We move all terms to the left:
-2x(3x-1)-(-6x-1)=0
We multiply parentheses
-6x^2+2x-(-6x-1)=0
We get rid of parentheses
-6x^2+2x+6x+1=0
We add all the numbers together, and all the variables
-6x^2+8x+1=0
a = -6; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-6)·1
Δ = 88
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*-6}=\frac{-8-2\sqrt{22}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*-6}=\frac{-8+2\sqrt{22}}{-12} $
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