2x+1=3/4x-9

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

2x+1=3/4x-9

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

2x-3/4x+9+1=0

We multiply all the terms by the denominator


2x*4x+9*4x+1*4x-3=0

Wy multiply elements

8x^2+36x+4x-3=0

We add all the numbers together, and all the variables

8x^2+40x-3=0

a = 8; b = 40; c = -3;
Δ = b2-4ac
Δ = 402-4·8·(-3)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{106}}{2*8}=\frac{-40-4\sqrt{106}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{106}}{2*8}=\frac{-40+4\sqrt{106}}{16}
$