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5x+2x^2=48
We move all terms to the left:
5x+2x^2-(48)=0
a = 2; b = 5; c = -48;
Δ = b2-4ac
Δ = 52-4·2·(-48)
Δ = 409
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{409}}{2*2}=\frac{-5-\sqrt{409}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{409}}{2*2}=\frac{-5+\sqrt{409}}{4} $
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