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2(x2+6x-1)+2x-3=
We move all terms to the left:
2(x2+6x-1)+2x-3-()=0
We add all the numbers together, and all the variables
2(+x^2+6x-1)+2x-3-()=0
We add all the numbers together, and all the variables
2(+x^2+6x-1)+2x=0
We multiply parentheses
2x^2+12x+2x-2=0
We add all the numbers together, and all the variables
2x^2+14x-2=0
a = 2; b = 14; c = -2;
Δ = b2-4ac
Δ = 142-4·2·(-2)
Δ = 212
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{53}}{2*2}=\frac{-14-2\sqrt{53}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{53}}{2*2}=\frac{-14+2\sqrt{53}}{4} $
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