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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

4x+(+3/2)x-144=0

We multiply parentheses

3x^2+4x-144=0

a = 3; b = 4; c = -144;
Δ = b2-4ac
Δ = 42-4·3·(-144)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{109}}{2*3}=\frac{-4-4\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{109}}{2*3}=\frac{-4+4\sqrt{109}}{6}
$