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6x^2+2x-14=49-45x
We move all terms to the left:
6x^2+2x-14-(49-45x)=0
We add all the numbers together, and all the variables
6x^2+2x-(-45x+49)-14=0
We get rid of parentheses
6x^2+2x+45x-49-14=0
We add all the numbers together, and all the variables
6x^2+47x-63=0
a = 6; b = 47; c = -63;
Δ = b2-4ac
Δ = 472-4·6·(-63)
Δ = 3721
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{3721}=61$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-61}{2*6}=\frac{-108}{12} =-9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+61}{2*6}=\frac{14}{12} =1+1/6 $
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