1/2*4x-1*3x=180

Solution for 1/2*4x-1*3x=180 equation:

1/2*4x-1*3x=180

We move all terms to the left:

1/2*4x-1*3x-(180)=0


Domain of the equation: 2*4x!=0

x!=0/1

x!=0

x∈R


Wy multiply elements

1/2*4x-3x-180=0

We multiply all the terms by the denominator


-3x*2*4x-180*2*4x+1=0

Wy multiply elements

-24x^2*4-1440x*4+1=0

Wy multiply elements

-96x^2-5760x+1=0

a = -96; b = -5760; c = +1;
Δ = b2-4ac
Δ = -57602-4·(-96)·1
Δ = 33177984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{33177984}=\sqrt{64*518406}=\sqrt{64}*\sqrt{518406}=8\sqrt{518406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5760)-8\sqrt{518406}}{2*-96}=\frac{5760-8\sqrt{518406}}{-192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5760)+8\sqrt{518406}}{2*-96}=\frac{5760+8\sqrt{518406}}{-192}
$