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12x^2-6x-27=-7
We move all terms to the left:
12x^2-6x-27-(-7)=0
We add all the numbers together, and all the variables
12x^2-6x-20=0
a = 12; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·12·(-20)
Δ = 996
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{249}}{2*12}=\frac{6-2\sqrt{249}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{249}}{2*12}=\frac{6+2\sqrt{249}}{24} $
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