3/4x+2x-3=-14x+21

Solution for 3/4x+2x-3=-14x+21 equation:

3/4x+2x-3=-14x+21

We move all terms to the left:

3/4x+2x-3-(-14x+21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-(-14x+21)-3=0

We get rid of parentheses

2x+3/4x+14x-21-3=0

We multiply all the terms by the denominator


2x*4x+14x*4x-21*4x-3*4x+3=0

Wy multiply elements

8x^2+56x^2-84x-12x+3=0

We add all the numbers together, and all the variables

64x^2-96x+3=0

a = 64; b = -96; c = +3;
Δ = b2-4ac
Δ = -962-4·64·3
Δ = 8448
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:

$\sqrt{\Delta}=\sqrt{8448}=\sqrt{256*33}=\sqrt{256}*\sqrt{33}=16\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{33}}{2*64}=\frac{96-16\sqrt{33}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{33}}{2*64}=\frac{96+16\sqrt{33}}{128}
$