3/4x-9x=-20

Solution for 3/4x-9x=-20 equation:

3/4x-9x=-20

We move all terms to the left:

3/4x-9x-(-20)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+3/4x+20=0

We multiply all the terms by the denominator


-9x*4x+20*4x+3=0

Wy multiply elements

-36x^2+80x+3=0

a = -36; b = 80; c = +3;
Δ = b2-4ac
Δ = 802-4·(-36)·3
Δ = 6832
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:

$\sqrt{\Delta}=\sqrt{6832}=\sqrt{16*427}=\sqrt{16}*\sqrt{427}=4\sqrt{427}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{427}}{2*-36}=\frac{-80-4\sqrt{427}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{427}}{2*-36}=\frac{-80+4\sqrt{427}}{-72}
$