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4x^2+58x+208=460
We move all terms to the left:
4x^2+58x+208-(460)=0
We add all the numbers together, and all the variables
4x^2+58x-252=0
a = 4; b = 58; c = -252;
Δ = b2-4ac
Δ = 582-4·4·(-252)
Δ = 7396
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{7396}=86$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-86}{2*4}=\frac{-144}{8} =-18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+86}{2*4}=\frac{28}{8} =3+1/2 $
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