(14x^2+7x-4)/(-7x^2+5)=0

Solution for (14x^2+7x-4)/(-7x^2+5)=0 equation:

(14x^2+7x-4)/(-7x^2+5)=0


Domain of the equation: (-7x^2+5)!=0

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

-7x^2!=-5

x^2!=-5/-7

x^2!=√5/7

x!=2.2360679775

x∈R


We multiply all the terms by the denominator


(14x^2+7x-4)=0

We get rid of parentheses

14x^2+7x-4=0

a = 14; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·14·(-4)
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{273}}{2*14}=\frac{-7-\sqrt{273}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{273}}{2*14}=\frac{-7+\sqrt{273}}{28}
$