5/2x+4=7/10x-8

Solution for 5/2x+4=7/10x-8 equation:

5/2x+4=7/10x-8

We move all terms to the left:

5/2x+4-(7/10x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x-8)!=0

x∈R


We get rid of parentheses

5/2x-7/10x+8+4=0

We calculate fractions


50x/20x^2+(-14x)/20x^2+8+4=0

We add all the numbers together, and all the variables

50x/20x^2+(-14x)/20x^2+12=0

We multiply all the terms by the denominator


50x+(-14x)+12*20x^2=0

Wy multiply elements

240x^2+50x+(-14x)=0

We get rid of parentheses

240x^2+50x-14x=0

We add all the numbers together, and all the variables

240x^2+36x=0

a = 240; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·240·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*240}=\frac{-72}{480}
=-3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*240}=\frac{0}{480}
=0
$