05x-3=3/4x+4

Solution for 05x-3=3/4x+4 equation:

05x-3=3/4x+4

We move all terms to the left:

05x-3-(3/4x+4)=0


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

x∈R


We get rid of parentheses

05x-3/4x-4-3=0

We multiply all the terms by the denominator


05x*4x-4*4x-3*4x-3=0

Wy multiply elements

20x^2-16x-12x-3=0

We add all the numbers together, and all the variables

20x^2-28x-3=0

a = 20; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·20·(-3)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-32}{2*20}=\frac{-4}{40}
=-1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+32}{2*20}=\frac{60}{40}
=1+1/2
$