3/5x+11.8=3x-5

Solution for 3/5x+11.8=3x-5 equation:

3/5x+11.8=3x-5

We move all terms to the left:

3/5x+11.8-(3x-5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-3x+5+11.8=0

We multiply all the terms by the denominator


-3x*5x+5*5x+(11.8)*5x+3=0

We multiply parentheses

-3x*5x+5*5x+59x+3=0

Wy multiply elements

-15x^2+25x+59x+3=0

We add all the numbers together, and all the variables

-15x^2+84x+3=0

a = -15; b = 84; c = +3;
Δ = b2-4ac
Δ = 842-4·(-15)·3
Δ = 7236
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:

$\sqrt{\Delta}=\sqrt{7236}=\sqrt{36*201}=\sqrt{36}*\sqrt{201}=6\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-6\sqrt{201}}{2*-15}=\frac{-84-6\sqrt{201}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+6\sqrt{201}}{2*-15}=\frac{-84+6\sqrt{201}}{-30}
$