(-4x^2+5)/(3x^2-14x-5)=0

Solution for (-4x^2+5)/(3x^2-14x-5)=0 equation:

(-4x^2+5)/(3x^2-14x-5)=0


Domain of the equation: (3x^2-14x-5)!=0

We move all terms containing x to the left, all other terms to the right

3x^2-14x!=5

x∈R


We multiply all the terms by the denominator


(-4x^2+5)=0

We get rid of parentheses

-4x^2+5=0

a = -4; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-4)·5
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*-4}=\frac{0-4\sqrt{5}}{-8}
=-\frac{4\sqrt{5}}{-8}
=-\frac{\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*-4}=\frac{0+4\sqrt{5}}{-8}
=\frac{4\sqrt{5}}{-8}
=\frac{\sqrt{5}}{-2}
$