9x-156=3/2x+36

Solution for 9x-156=3/2x+36 equation:

9x-156=3/2x+36

We move all terms to the left:

9x-156-(3/2x+36)=0


Domain of the equation: 2x+36)!=0

x∈R


We get rid of parentheses

9x-3/2x-36-156=0

We multiply all the terms by the denominator


9x*2x-36*2x-156*2x-3=0

Wy multiply elements

18x^2-72x-312x-3=0

We add all the numbers together, and all the variables

18x^2-384x-3=0

a = 18; b = -384; c = -3;
Δ = b2-4ac
Δ = -3842-4·18·(-3)
Δ = 147672
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:

$\sqrt{\Delta}=\sqrt{147672}=\sqrt{36*4102}=\sqrt{36}*\sqrt{4102}=6\sqrt{4102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-6\sqrt{4102}}{2*18}=\frac{384-6\sqrt{4102}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+6\sqrt{4102}}{2*18}=\frac{384+6\sqrt{4102}}{36}
$