-3/4x-2+3x=-4x+5

Solution for -3/4x-2+3x=-4x+5 equation:

-3/4x-2+3x=-4x+5

We move all terms to the left:

-3/4x-2+3x-(-4x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x-3/4x-(-4x+5)-2=0

We get rid of parentheses

3x-3/4x+4x-5-2=0

We multiply all the terms by the denominator


3x*4x+4x*4x-5*4x-2*4x-3=0

Wy multiply elements

12x^2+16x^2-20x-8x-3=0

We add all the numbers together, and all the variables

28x^2-28x-3=0

a = 28; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·28·(-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{-(-28)-4\sqrt{70}}{2*28}=\frac{28-4\sqrt{70}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{70}}{2*28}=\frac{28+4\sqrt{70}}{56}
$