1=-1.4x+5+3/4x

Solution for 1=-1.4x+5+3/4x equation:

1=-1.4x+5+3/4x

We move all terms to the left:

1-(-1.4x+5+3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(-1.4x+3/4x+5)+1=0

We get rid of parentheses

1.4x-3/4x-5+1=0

We multiply all the terms by the denominator


(1.4x)*4x-5*4x+1*4x-3=0

We add all the numbers together, and all the variables

(+1.4x)*4x-5*4x+1*4x-3=0

We multiply parentheses

4x^2-5*4x+1*4x-3=0

Wy multiply elements

4x^2-20x+4x-3=0

We add all the numbers together, and all the variables

4x^2-16x-3=0

a = 4; b = -16; c = -3;
Δ = b2-4ac
Δ = -162-4·4·(-3)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*4}=\frac{16-4\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*4}=\frac{16+4\sqrt{19}}{8}
$