76/4x-5=5*17x

Solution for 76/4x-5=5*17x equation:

76/4x-5=5*17x

We move all terms to the left:

76/4x-5-(5*17x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

76/4x-(+5*17x)-5=0

We get rid of parentheses

76/4x-5*17x-5=0

We multiply all the terms by the denominator


-(5*17x)*4x-5*4x+76=0

We add all the numbers together, and all the variables

-(+5*17x)*4x-5*4x+76=0

We multiply parentheses

-340x^2-5*4x+76=0

Wy multiply elements

-340x^2-20x+76=0

a = -340; b = -20; c = +76;
Δ = b2-4ac
Δ = -202-4·(-340)·76
Δ = 103760
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:

$\sqrt{\Delta}=\sqrt{103760}=\sqrt{16*6485}=\sqrt{16}*\sqrt{6485}=4\sqrt{6485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{6485}}{2*-340}=\frac{20-4\sqrt{6485}}{-680}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{6485}}{2*-340}=\frac{20+4\sqrt{6485}}{-680}
$