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2x(3x-6)+4x-2=8+2x
We move all terms to the left:
2x(3x-6)+4x-2-(8+2x)=0
We add all the numbers together, and all the variables
2x(3x-6)+4x-(2x+8)-2=0
We add all the numbers together, and all the variables
4x+2x(3x-6)-(2x+8)-2=0
We multiply parentheses
6x^2+4x-12x-(2x+8)-2=0
We get rid of parentheses
6x^2+4x-12x-2x-8-2=0
We add all the numbers together, and all the variables
6x^2-10x-10=0
a = 6; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·6·(-10)
Δ = 340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*6}=\frac{10-2\sqrt{85}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*6}=\frac{10+2\sqrt{85}}{12} $
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