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(3x+19)5x=115
We move all terms to the left:
(3x+19)5x-(115)=0
We multiply parentheses
15x^2+95x-115=0
a = 15; b = 95; c = -115;
Δ = b2-4ac
Δ = 952-4·15·(-115)
Δ = 15925
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15925}=\sqrt{1225*13}=\sqrt{1225}*\sqrt{13}=35\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-35\sqrt{13}}{2*15}=\frac{-95-35\sqrt{13}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+35\sqrt{13}}{2*15}=\frac{-95+35\sqrt{13}}{30} $
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