3/4x-4+1/2x=21

Solution for 3/4x-4+1/2x=21 equation:

3/4x-4+1/2x=21

We move all terms to the left:

3/4x-4+1/2x-(21)=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 add all the numbers together, and all the variables

3/4x+1/2x-25=0

We calculate fractions


6x/8x^2+4x/8x^2-25=0

We multiply all the terms by the denominator


6x+4x-25*8x^2=0

We add all the numbers together, and all the variables

10x-25*8x^2=0

Wy multiply elements

-200x^2+10x=0

a = -200; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-200)·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*-200}=\frac{-20}{-400}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-200}=\frac{0}{-400}
=0
$