3x-27=7/5x+5

Solution for 3x-27=7/5x+5 equation:

3x-27=7/5x+5

We move all terms to the left:

3x-27-(7/5x+5)=0


Domain of the equation: 5x+5)!=0

x∈R


We get rid of parentheses

3x-7/5x-5-27=0

We multiply all the terms by the denominator


3x*5x-5*5x-27*5x-7=0

Wy multiply elements

15x^2-25x-135x-7=0

We add all the numbers together, and all the variables

15x^2-160x-7=0

a = 15; b = -160; c = -7;
Δ = b2-4ac
Δ = -1602-4·15·(-7)
Δ = 26020
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:

$\sqrt{\Delta}=\sqrt{26020}=\sqrt{4*6505}=\sqrt{4}*\sqrt{6505}=2\sqrt{6505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-2\sqrt{6505}}{2*15}=\frac{160-2\sqrt{6505}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+2\sqrt{6505}}{2*15}=\frac{160+2\sqrt{6505}}{30}
$