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6x^2-6x-114=2x^2+2x+3
We move all terms to the left:
6x^2-6x-114-(2x^2+2x+3)=0
We get rid of parentheses
6x^2-2x^2-6x-2x-3-114=0
We add all the numbers together, and all the variables
4x^2-8x-117=0
a = 4; b = -8; c = -117;
Δ = b2-4ac
Δ = -82-4·4·(-117)
Δ = 1936
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{1936}=44$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-44}{2*4}=\frac{-36}{8} =-4+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+44}{2*4}=\frac{52}{8} =6+1/2 $
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