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5x+3x^2=4x+18
We move all terms to the left:
5x+3x^2-(4x+18)=0
We get rid of parentheses
3x^2+5x-4x-18=0
We add all the numbers together, and all the variables
3x^2+x-18=0
a = 3; b = 1; c = -18;
Δ = b2-4ac
Δ = 12-4·3·(-18)
Δ = 217
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{-(1)-\sqrt{217}}{2*3}=\frac{-1-\sqrt{217}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{217}}{2*3}=\frac{-1+\sqrt{217}}{6} $
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