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5x+34=3x^2
We move all terms to the left:
5x+34-(3x^2)=0
determiningTheFunctionDomain -3x^2+5x+34=0
a = -3; b = 5; c = +34;
Δ = b2-4ac
Δ = 52-4·(-3)·34
Δ = 433
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{-(5)-\sqrt{433}}{2*-3}=\frac{-5-\sqrt{433}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{433}}{2*-3}=\frac{-5+\sqrt{433}}{-6} $
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