3/4x-17-3x-13=90

Solution for 3/4x-17-3x-13=90 equation:

3/4x-17-3x-13=90

We move all terms to the left:

3/4x-17-3x-13-(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

-3x+3/4x-120=0

We multiply all the terms by the denominator


-3x*4x-120*4x+3=0

Wy multiply elements

-12x^2-480x+3=0

a = -12; b = -480; c = +3;
Δ = b2-4ac
Δ = -4802-4·(-12)·3
Δ = 230544
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:

$\sqrt{\Delta}=\sqrt{230544}=\sqrt{144*1601}=\sqrt{144}*\sqrt{1601}=12\sqrt{1601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-12\sqrt{1601}}{2*-12}=\frac{480-12\sqrt{1601}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+12\sqrt{1601}}{2*-12}=\frac{480+12\sqrt{1601}}{-24}
$