3/5x+7=8+0.6x

Solution for 3/5x+7=8+0.6x equation:

3/5x+7=8+0.6x

We move all terms to the left:

3/5x+7-(8+0.6x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(0.6x+8)+7=0

We get rid of parentheses

3/5x-0.6x-8+7=0

We multiply all the terms by the denominator


-(0.6x)*5x-8*5x+7*5x+3=0

We add all the numbers together, and all the variables

-(+0.6x)*5x-8*5x+7*5x+3=0

We multiply parentheses

-0x^2-8*5x+7*5x+3=0

Wy multiply elements

-0x^2-40x+35x+3=0

We add all the numbers together, and all the variables

-1x^2-5x+3=0

a = -1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-1)·3
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{37}}{2*-1}=\frac{5-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{37}}{2*-1}=\frac{5+\sqrt{37}}{-2}
$