4/5x+7=3/15x-3

Solution for 4/5x+7=3/15x-3 equation:

4/5x+7=3/15x-3

We move all terms to the left:

4/5x+7-(3/15x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x-3)!=0

x∈R


We get rid of parentheses

4/5x-3/15x+3+7=0

We calculate fractions


60x/75x^2+(-15x)/75x^2+3+7=0

We add all the numbers together, and all the variables

60x/75x^2+(-15x)/75x^2+10=0

We multiply all the terms by the denominator


60x+(-15x)+10*75x^2=0

Wy multiply elements

750x^2+60x+(-15x)=0

We get rid of parentheses

750x^2+60x-15x=0

We add all the numbers together, and all the variables

750x^2+45x=0

a = 750; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·750·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*750}=\frac{-90}{1500}
=-3/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*750}=\frac{0}{1500}
=0
$