-3/4x-1/2x=10

Solution for -3/4x-1/2x=10 equation:

-3/4x-1/2x=10

We move all terms to the left:

-3/4x-1/2x-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


(-6x)/8x^2+(-4x)/8x^2-10=0

We multiply all the terms by the denominator


(-6x)+(-4x)-10*8x^2=0

Wy multiply elements

-80x^2+(-6x)+(-4x)=0

We get rid of parentheses

-80x^2-6x-4x=0

We add all the numbers together, and all the variables

-80x^2-10x=0

a = -80; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-80)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-80}=\frac{0}{-160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-80}=\frac{20}{-160}
=-1/8
$