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7x^2-6x-11=3x^2
We move all terms to the left:
7x^2-6x-11-(3x^2)=0
determiningTheFunctionDomain 7x^2-3x^2-6x-11=0
We add all the numbers together, and all the variables
4x^2-6x-11=0
a = 4; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·4·(-11)
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{-(-6)-2\sqrt{53}}{2*4}=\frac{6-2\sqrt{53}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{53}}{2*4}=\frac{6+2\sqrt{53}}{8} $
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