3/4xX+1/2xx=180

Solution for 3/4xX+1/2xx=180 equation:

3/4xx+1/2xx=180

We move all terms to the left:

3/4xx+1/2xx-(180)=0


Domain of the equation: 4xx!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2xx!=0

x!=0/1

x!=0

x∈R


We calculate fractions


6x/8x^2+4x/8x^2-180=0

We multiply all the terms by the denominator


6x+4x-180*8x^2=0

We add all the numbers together, and all the variables

10x-180*8x^2=0

Wy multiply elements

-1440x^2+10x=0

a = -1440; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-1440)·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*-1440}=\frac{-20}{-2880}
=1/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-1440}=\frac{0}{-2880}
=0
$