3/4x-9=15x-15

Solution for 3/4x-9=15x-15 equation:

3/4x-9=15x-15

We move all terms to the left:

3/4x-9-(15x-15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-15x+15-9=0

We multiply all the terms by the denominator


-15x*4x+15*4x-9*4x+3=0

Wy multiply elements

-60x^2+60x-36x+3=0

We add all the numbers together, and all the variables

-60x^2+24x+3=0

a = -60; b = 24; c = +3;
Δ = b2-4ac
Δ = 242-4·(-60)·3
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-36}{2*-60}=\frac{-60}{-120}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+36}{2*-60}=\frac{12}{-120}
=-1/10
$