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12x+5x^2=81
We move all terms to the left:
12x+5x^2-(81)=0
a = 5; b = 12; c = -81;
Δ = b2-4ac
Δ = 122-4·5·(-81)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-42}{2*5}=\frac{-54}{10} =-5+2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+42}{2*5}=\frac{30}{10} =3 $
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