4x+3+3/2x+33=180

Solution for 4x+3+3/2x+33=180 equation:

4x+3+3/2x+33=180

We move all terms to the left:

4x+3+3/2x+33-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+3/2x-144=0

We multiply all the terms by the denominator


4x*2x-144*2x+3=0

Wy multiply elements

8x^2-288x+3=0

a = 8; b = -288; c = +3;
Δ = b2-4ac
Δ = -2882-4·8·3
Δ = 82848
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:

$\sqrt{\Delta}=\sqrt{82848}=\sqrt{16*5178}=\sqrt{16}*\sqrt{5178}=4\sqrt{5178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-4\sqrt{5178}}{2*8}=\frac{288-4\sqrt{5178}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+4\sqrt{5178}}{2*8}=\frac{288+4\sqrt{5178}}{16}
$