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X-5=12-2X^2
We move all terms to the left:
X-5-(12-2X^2)=0
We get rid of parentheses
2X^2+X-12-5=0
We add all the numbers together, and all the variables
2X^2+X-17=0
a = 2; b = 1; c = -17;
Δ = b2-4ac
Δ = 12-4·2·(-17)
Δ = 137
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{137}}{2*2}=\frac{-1-\sqrt{137}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{137}}{2*2}=\frac{-1+\sqrt{137}}{4} $
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