3/5x-15=6-5x+12

Solution for 3/5x-15=6-5x+12 equation:

3/5x-15=6-5x+12

We move all terms to the left:

3/5x-15-(6-5x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(-5x+18)-15=0

We get rid of parentheses

3/5x+5x-18-15=0

We multiply all the terms by the denominator


5x*5x-18*5x-15*5x+3=0

Wy multiply elements

25x^2-90x-75x+3=0

We add all the numbers together, and all the variables

25x^2-165x+3=0

a = 25; b = -165; c = +3;
Δ = b2-4ac
Δ = -1652-4·25·3
Δ = 26925
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:

$\sqrt{\Delta}=\sqrt{26925}=\sqrt{25*1077}=\sqrt{25}*\sqrt{1077}=5\sqrt{1077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-5\sqrt{1077}}{2*25}=\frac{165-5\sqrt{1077}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+5\sqrt{1077}}{2*25}=\frac{165+5\sqrt{1077}}{50}
$