3/4x-133x-17=90

Solution for 3/4x-133x-17=90 equation:

3/4x-133x-17=90

We move all terms to the left:

3/4x-133x-17-(90)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-133x+3/4x-107=0

We multiply all the terms by the denominator


-133x*4x-107*4x+3=0

Wy multiply elements

-532x^2-428x+3=0

a = -532; b = -428; c = +3;
Δ = b2-4ac
Δ = -4282-4·(-532)·3
Δ = 189568
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:

$\sqrt{\Delta}=\sqrt{189568}=\sqrt{64*2962}=\sqrt{64}*\sqrt{2962}=8\sqrt{2962}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-428)-8\sqrt{2962}}{2*-532}=\frac{428-8\sqrt{2962}}{-1064}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-428)+8\sqrt{2962}}{2*-532}=\frac{428+8\sqrt{2962}}{-1064}
$