8-x/5x+60=3x-7

Solution for 8-x/5x+60=3x-7 equation:

8-x/5x+60=3x-7

We move all terms to the left:

8-x/5x+60-(3x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-x/5x-(3x-7)+68=0

We get rid of parentheses

-x/5x-3x+7+68=0

We multiply all the terms by the denominator


-x-3x*5x+7*5x+68*5x=0

We add all the numbers together, and all the variables

-1x-3x*5x+7*5x+68*5x=0

Wy multiply elements

-15x^2-1x+35x+340x=0

We add all the numbers together, and all the variables

-15x^2+374x=0

a = -15; b = 374; c = 0;
Δ = b2-4ac
Δ = 3742-4·(-15)·0
Δ = 139876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{139876}=374$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(374)-374}{2*-15}=\frac{-748}{-30}
=24+14/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(374)+374}{2*-15}=\frac{0}{-30}
=0
$