x=-3/4x+-3

Solution for x=-3/4x+-3 equation:

x=-3/4x+-3

We move all terms to the left:

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


Domain of the equation: 4x+-3)!=0

x∈R


We add all the numbers together, and all the variables

x-(-3/4x-3)=0

We get rid of parentheses

x+3/4x+3=0

We multiply all the terms by the denominator


x*4x+3*4x+3=0

Wy multiply elements

4x^2+12x+3=0

a = 4; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·4·3
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*4}=\frac{-12-4\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*4}=\frac{-12+4\sqrt{6}}{8}
$