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77+14x-39=19x^2
We move all terms to the left:
77+14x-39-(19x^2)=0
determiningTheFunctionDomain -19x^2+14x+77-39=0
We add all the numbers together, and all the variables
-19x^2+14x+38=0
a = -19; b = 14; c = +38;
Δ = b2-4ac
Δ = 142-4·(-19)·38
Δ = 3084
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3084}=\sqrt{4*771}=\sqrt{4}*\sqrt{771}=2\sqrt{771}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{771}}{2*-19}=\frac{-14-2\sqrt{771}}{-38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{771}}{2*-19}=\frac{-14+2\sqrt{771}}{-38} $
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