4.2x-1=3/4x+9

Solution for 4.2x-1=3/4x+9 equation:

4.2x-1=3/4x+9

We move all terms to the left:

4.2x-1-(3/4x+9)=0


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

x∈R


We get rid of parentheses

4.2x-3/4x-9-1=0

We multiply all the terms by the denominator


(4.2x)*4x-9*4x-1*4x-3=0

We add all the numbers together, and all the variables

(+4.2x)*4x-9*4x-1*4x-3=0

We multiply parentheses

16x^2-9*4x-1*4x-3=0

Wy multiply elements

16x^2-36x-4x-3=0

We add all the numbers together, and all the variables

16x^2-40x-3=0

a = 16; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·16·(-3)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16\sqrt{7}}{2*16}=\frac{40-16\sqrt{7}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16\sqrt{7}}{2*16}=\frac{40+16\sqrt{7}}{32}
$