4x=40-3/5x-3

Solution for 4x=40-3/5x-3 equation:

4x=40-3/5x-3

We move all terms to the left:

4x-(40-3/5x-3)=0


Domain of the equation: 5x-3)!=0

x∈R


We add all the numbers together, and all the variables

4x-(-3/5x+37)=0

We get rid of parentheses

4x+3/5x-37=0

We multiply all the terms by the denominator


4x*5x-37*5x+3=0

Wy multiply elements

20x^2-185x+3=0

a = 20; b = -185; c = +3;
Δ = b2-4ac
Δ = -1852-4·20·3
Δ = 33985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-185)-\sqrt{33985}}{2*20}=\frac{185-\sqrt{33985}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-185)+\sqrt{33985}}{2*20}=\frac{185+\sqrt{33985}}{40}
$