-3/5x-7/10x+5/10x=-56

Solution for -3/5x-7/10x+5/10x=-56 equation:

-3/5x-7/10x+5/10x=-56

We move all terms to the left:

-3/5x-7/10x+5/10x-(-56)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-7/10x+5/10x+56=0

We calculate fractions


(-30x)/50x^2+(25x-7)/50x^2+56=0

We multiply all the terms by the denominator


(-30x)+(25x-7)+56*50x^2=0

Wy multiply elements

2800x^2+(-30x)+(25x-7)=0

We get rid of parentheses

2800x^2-30x+25x-7=0

We add all the numbers together, and all the variables

2800x^2-5x-7=0

a = 2800; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·2800·(-7)
Δ = 78425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{78425}=\sqrt{25*3137}=\sqrt{25}*\sqrt{3137}=5\sqrt{3137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{3137}}{2*2800}=\frac{5-5\sqrt{3137}}{5600}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{3137}}{2*2800}=\frac{5+5\sqrt{3137}}{5600}
$