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6x+4x^2=108
We move all terms to the left:
6x+4x^2-(108)=0
a = 4; b = 6; c = -108;
Δ = b2-4ac
Δ = 62-4·4·(-108)
Δ = 1764
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{1764}=42$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-42}{2*4}=\frac{-48}{8} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+42}{2*4}=\frac{36}{8} =4+1/2 $
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