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-3+7x(2)=6-14x
We move all terms to the left:
-3+7x(2)-(6-14x)=0
We add all the numbers together, and all the variables
7x2-(-14x+6)-3=0
We add all the numbers together, and all the variables
7x^2-(-14x+6)-3=0
We get rid of parentheses
7x^2+14x-6-3=0
We add all the numbers together, and all the variables
7x^2+14x-9=0
a = 7; b = 14; c = -9;
Δ = b2-4ac
Δ = 142-4·7·(-9)
Δ = 448
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{7}}{2*7}=\frac{-14-8\sqrt{7}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{7}}{2*7}=\frac{-14+8\sqrt{7}}{14} $
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