10-3/4x+7+5/8x=27

Solution for 10-3/4x+7+5/8x=27 equation:

10-3/4x+7+5/8x=27

We move all terms to the left:

10-3/4x+7+5/8x-(27)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-320x^2+20x+(-24x)=0

We get rid of parentheses

-320x^2+20x-24x=0

We add all the numbers together, and all the variables

-320x^2-4x=0

a = -320; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-320)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-320}=\frac{0}{-640}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-320}=\frac{8}{-640}
=-1/80
$