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4x+(15x^2)=110
We move all terms to the left:
4x+(15x^2)-(110)=0
determiningTheFunctionDomain 15x^2+4x-110=0
a = 15; b = 4; c = -110;
Δ = b2-4ac
Δ = 42-4·15·(-110)
Δ = 6616
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6616}=\sqrt{4*1654}=\sqrt{4}*\sqrt{1654}=2\sqrt{1654}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{1654}}{2*15}=\frac{-4-2\sqrt{1654}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{1654}}{2*15}=\frac{-4+2\sqrt{1654}}{30} $
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