1/2x=-3/4x+9

Solution for 1/2x=-3/4x+9 equation:

1/2x=-3/4x+9

We move all terms to the left:

1/2x-(-3/4x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+9)!=0

x∈R


We get rid of parentheses

1/2x+3/4x-9=0

We calculate fractions


4x/8x^2+6x/8x^2-9=0

We multiply all the terms by the denominator


4x+6x-9*8x^2=0

We add all the numbers together, and all the variables

10x-9*8x^2=0

Wy multiply elements

-72x^2+10x=0

a = -72; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-72)·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*-72}=\frac{-20}{-144}
=5/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-72}=\frac{0}{-144}
=0
$