-3/4x+1=5/8x-10

Solution for -3/4x+1=5/8x-10 equation:

-3/4x+1=5/8x-10

We move all terms to the left:

-3/4x+1-(5/8x-10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

-3/4x-5/8x+10+1=0

We calculate fractions


(-24x)/32x^2+(-20x)/32x^2+10+1=0

We add all the numbers together, and all the variables

(-24x)/32x^2+(-20x)/32x^2+11=0

We multiply all the terms by the denominator


(-24x)+(-20x)+11*32x^2=0

Wy multiply elements

352x^2+(-24x)+(-20x)=0

We get rid of parentheses

352x^2-24x-20x=0

We add all the numbers together, and all the variables

352x^2-44x=0

a = 352; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·352·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*352}=\frac{0}{704}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*352}=\frac{88}{704}
=1/8
$