23/5x-8=-1.4x+16

Solution for 23/5x-8=-1.4x+16 equation:

23/5x-8=-1.4x+16

We move all terms to the left:

23/5x-8-(-1.4x+16)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

23/5x+1.4x-16-8=0

We multiply all the terms by the denominator


(1.4x)*5x-16*5x-8*5x+23=0

We add all the numbers together, and all the variables

(+1.4x)*5x-16*5x-8*5x+23=0

We multiply parentheses

5x^2-16*5x-8*5x+23=0

Wy multiply elements

5x^2-80x-40x+23=0

We add all the numbers together, and all the variables

5x^2-120x+23=0

a = 5; b = -120; c = +23;
Δ = b2-4ac
Δ = -1202-4·5·23
Δ = 13940
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:

$\sqrt{\Delta}=\sqrt{13940}=\sqrt{4*3485}=\sqrt{4}*\sqrt{3485}=2\sqrt{3485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3485}}{2*5}=\frac{120-2\sqrt{3485}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3485}}{2*5}=\frac{120+2\sqrt{3485}}{10}
$