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25.12x+4.19x^2=37.68
We move all terms to the left:
25.12x+4.19x^2-(37.68)=0
We add all the numbers together, and all the variables
4.19x^2+25.12x-37.68=0
a = 4.19; b = 25.12; c = -37.68;
Δ = b2-4ac
Δ = 25.122-4·4.19·(-37.68)
Δ = 1262.5312
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{-(25.12)-\sqrt{1262.5312}}{2*4.19}=\frac{-25.12-\sqrt{1262.5312}}{8.38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25.12)+\sqrt{1262.5312}}{2*4.19}=\frac{-25.12+\sqrt{1262.5312}}{8.38} $
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