7/10x-3/5x+2=8

Solution for 7/10x-3/5x+2=8 equation:

7/10x-3/5x+2=8

We move all terms to the left:

7/10x-3/5x+2-(8)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7/10x-3/5x-6=0

We calculate fractions


35x/50x^2+(-30x)/50x^2-6=0

We multiply all the terms by the denominator


35x+(-30x)-6*50x^2=0

Wy multiply elements

-300x^2+35x+(-30x)=0

We get rid of parentheses

-300x^2+35x-30x=0

We add all the numbers together, and all the variables

-300x^2+5x=0

a = -300; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-300)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-300}=\frac{-10}{-600}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-300}=\frac{0}{-600}
=0
$