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-16x^2+48x+10=39

We move all terms to the left:

-16x^2+48x+10-(39)=0

We add all the numbers together, and all the variables

-16x^2+48x-29=0

a = -16; b = 48; c = -29;

Δ = b^{2}-4ac

Δ = 48^{2}-4·(-16)·(-29)

Δ = 448

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{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{7}}{2*-16}=\frac{-48-8\sqrt{7}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{7}}{2*-16}=\frac{-48+8\sqrt{7}}{-32} $

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