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^2-32x-3=0

a = 8; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·8·(-3)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{70}}{2*8}=\frac{32-4\sqrt{70}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{70}}{2*8}=\frac{32+4\sqrt{70}}{16}
$