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6x^2=12-6x-x2
We move all terms to the left:
6x^2-(12-6x-x2)=0
We add all the numbers together, and all the variables
6x^2-(-6x-1x^2+12)=0
We get rid of parentheses
6x^2+1x^2+6x-12=0
We add all the numbers together, and all the variables
7x^2+6x-12=0
a = 7; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·7·(-12)
Δ = 372
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{93}}{2*7}=\frac{-6-2\sqrt{93}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{93}}{2*7}=\frac{-6+2\sqrt{93}}{14} $
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