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2x(12-1x)=-6
We move all terms to the left:
2x(12-1x)-(-6)=0
We add all the numbers together, and all the variables
2x(-1x+12)-(-6)=0
We add all the numbers together, and all the variables
2x(-1x+12)+6=0
We multiply parentheses
-2x^2+24x+6=0
a = -2; b = 24; c = +6;
Δ = b2-4ac
Δ = 242-4·(-2)·6
Δ = 624
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{39}}{2*-2}=\frac{-24-4\sqrt{39}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{39}}{2*-2}=\frac{-24+4\sqrt{39}}{-4} $
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