-4/5x+15x=-5

Solution for -4/5x+15x=-5 equation:

-4/5x+15x=-5

We move all terms to the left:

-4/5x+15x-(-5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

15x-4/5x+5=0

We multiply all the terms by the denominator


15x*5x+5*5x-4=0

Wy multiply elements

75x^2+25x-4=0

a = 75; b = 25; c = -4;
Δ = b2-4ac
Δ = 252-4·75·(-4)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{73}}{2*75}=\frac{-25-5\sqrt{73}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{73}}{2*75}=\frac{-25+5\sqrt{73}}{150}
$