3/4r-(-1/2r)=-10

Solution for 3/4r-(-1/2r)=-10 equation:

3/4r-(-1/2r)=-10

We move all terms to the left:

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


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 2r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

3/4r-(-1/2r)+10=0

We get rid of parentheses

3/4r+1/2r+10=0

We calculate fractions


6r/8r^2+4r/8r^2+10=0

We multiply all the terms by the denominator


6r+4r+10*8r^2=0

We add all the numbers together, and all the variables

10r+10*8r^2=0

Wy multiply elements

80r^2+10r=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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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