-5/3x-7/2=1/5x-5

Solution for -5/3x-7/2=1/5x-5 equation:

-5/3x-7/2=1/5x-5

We move all terms to the left:

-5/3x-7/2-(1/5x-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

-5/3x-1/5x+5-7/2=0

We calculate fractions


(-525x^2)/60x^2+(-100x)/60x^2+(-12x)/60x^2+5=0

We multiply all the terms by the denominator


(-525x^2)+(-100x)+(-12x)+5*60x^2=0

Wy multiply elements

(-525x^2)+300x^2+(-100x)+(-12x)=0

We get rid of parentheses

-525x^2+300x^2-100x-12x=0

We add all the numbers together, and all the variables

-225x^2-112x=0

a = -225; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·(-225)·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*-225}=\frac{0}{-450}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*-225}=\frac{224}{-450}
=-112/225
$