3/4x-9=5x-60

Solution for 3/4x-9=5x-60 equation:

3/4x-9=5x-60

We move all terms to the left:

3/4x-9-(5x-60)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-5x+60-9=0

We multiply all the terms by the denominator


-5x*4x+60*4x-9*4x+3=0

Wy multiply elements

-20x^2+240x-36x+3=0

We add all the numbers together, and all the variables

-20x^2+204x+3=0

a = -20; b = 204; c = +3;
Δ = b2-4ac
Δ = 2042-4·(-20)·3
Δ = 41856
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:

$\sqrt{\Delta}=\sqrt{41856}=\sqrt{64*654}=\sqrt{64}*\sqrt{654}=8\sqrt{654}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(204)-8\sqrt{654}}{2*-20}=\frac{-204-8\sqrt{654}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(204)+8\sqrt{654}}{2*-20}=\frac{-204+8\sqrt{654}}{-40}
$