3x^2+5x^2-10x-16=0

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Solution for 3x^2+5x^2-10x-16=0 equation:



3x^2+5x^2-10x-16=0
We add all the numbers together, and all the variables
8x^2-10x-16=0
a = 8; b = -10; c = -16;
Δ = b2-4ac
Δ = -102-4·8·(-16)
Δ = 612
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:
$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{17}}{2*8}=\frac{10-6\sqrt{17}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{17}}{2*8}=\frac{10+6\sqrt{17}}{16} $

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