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

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## Solution for -16x^2+48x+10=39 equation:

-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 = b2-4acΔ = 482-4·(-16)·(-29)Δ = 448The delta value is higher than zero, so the equation has two solutionsWe 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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