340-9x-15x-(4/4x+1)=0

Solution for 340-9x-15x-(4/4x+1)=0 equation:

340-9x-15x-(4/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We add all the numbers together, and all the variables

-24x-(4/4x+1)+340=0

We get rid of parentheses

-24x-4/4x-1+340=0

We multiply all the terms by the denominator


-24x*4x-1*4x+340*4x-4=0

Wy multiply elements

-96x^2-4x+1360x-4=0

We add all the numbers together, and all the variables

-96x^2+1356x-4=0

a = -96; b = 1356; c = -4;
Δ = b2-4ac
Δ = 13562-4·(-96)·(-4)
Δ = 1837200
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:

$\sqrt{\Delta}=\sqrt{1837200}=\sqrt{400*4593}=\sqrt{400}*\sqrt{4593}=20\sqrt{4593}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1356)-20\sqrt{4593}}{2*-96}=\frac{-1356-20\sqrt{4593}}{-192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1356)+20\sqrt{4593}}{2*-96}=\frac{-1356+20\sqrt{4593}}{-192}
$