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3x^2+117=4x^2+4x
We move all terms to the left:
3x^2+117-(4x^2+4x)=0
We get rid of parentheses
3x^2-4x^2-4x+117=0
We add all the numbers together, and all the variables
-1x^2-4x+117=0
a = -1; b = -4; c = +117;
Δ = b2-4ac
Δ = -42-4·(-1)·117
Δ = 484
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{484}=22$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-22}{2*-1}=\frac{-18}{-2} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+22}{2*-1}=\frac{26}{-2} =-13 $
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