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6x^2+10x+7=11
We move all terms to the left:
6x^2+10x+7-(11)=0
We add all the numbers together, and all the variables
6x^2+10x-4=0
a = 6; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·6·(-4)
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*6}=\frac{-24}{12} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*6}=\frac{4}{12} =1/3 $
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