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15x+14x^2=2.94
We move all terms to the left:
15x+14x^2-(2.94)=0
We add all the numbers together, and all the variables
14x^2+15x-2.94=0
a = 14; b = 15; c = -2.94;
Δ = b2-4ac
Δ = 152-4·14·(-2.94)
Δ = 389.64
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{389.64}}{2*14}=\frac{-15-\sqrt{389.64}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{389.64}}{2*14}=\frac{-15+\sqrt{389.64}}{28} $
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