-3/5x-7/10+1/4x=-56

Solution for -3/5x-7/10+1/4x=-56 equation:

-3/5x-7/10+1/4x=-56

We move all terms to the left:

-3/5x-7/10+1/4x-(-56)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x+1/4x+56-7/10=0

We calculate fractions


(-560x^2)/200x^2+(-120x)/200x^2+50x/200x^2+56=0

We multiply all the terms by the denominator


(-560x^2)+(-120x)+50x+56*200x^2=0

We add all the numbers together, and all the variables

(-560x^2)+50x+(-120x)+56*200x^2=0

Wy multiply elements

(-560x^2)+11200x^2+50x+(-120x)=0

We get rid of parentheses

-560x^2+11200x^2+50x-120x=0

We add all the numbers together, and all the variables

10640x^2-70x=0

a = 10640; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·10640·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*10640}=\frac{0}{21280}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*10640}=\frac{140}{21280}
=1/152
$