2(1/4x+9)=3/4x-18

Solution for 2(1/4x+9)=3/4x-18 equation:

2(1/4x+9)=3/4x-18

We move all terms to the left:

2(1/4x+9)-(3/4x-18)=0


Domain of the equation: 4x+9)!=0

x∈R



Domain of the equation: 4x-18)!=0

x∈R


We multiply parentheses

2x-(3/4x-18)+18=0

We get rid of parentheses

2x-3/4x+18+18=0

We multiply all the terms by the denominator


2x*4x+18*4x+18*4x-3=0

Wy multiply elements

8x^2+72x+72x-3=0

We add all the numbers together, and all the variables

8x^2+144x-3=0

a = 8; b = 144; c = -3;
Δ = b2-4ac
Δ = 1442-4·8·(-3)
Δ = 20832
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:

$\sqrt{\Delta}=\sqrt{20832}=\sqrt{16*1302}=\sqrt{16}*\sqrt{1302}=4\sqrt{1302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1302}}{2*8}=\frac{-144-4\sqrt{1302}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1302}}{2*8}=\frac{-144+4\sqrt{1302}}{16}
$