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4x^2+14x-12=6
We move all terms to the left:
4x^2+14x-12-(6)=0
We add all the numbers together, and all the variables
4x^2+14x-18=0
a = 4; b = 14; c = -18;
Δ = b2-4ac
Δ = 142-4·4·(-18)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*4}=\frac{-36}{8} =-4+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*4}=\frac{8}{8} =1 $
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