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12x^2-5=-6x^2+3
We move all terms to the left:
12x^2-5-(-6x^2+3)=0
We get rid of parentheses
12x^2+6x^2-3-5=0
We add all the numbers together, and all the variables
18x^2-8=0
a = 18; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·18·(-8)
Δ = 576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{576}=24$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*18}=\frac{-24}{36} =-2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*18}=\frac{24}{36} =2/3 $
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