7/5x=x-4

Solution for 7/5x=x-4 equation:

7/5x=x-4

We move all terms to the left:

7/5x-(x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

7/5x-x+4=0

We multiply all the terms by the denominator


-x*5x+4*5x+7=0

Wy multiply elements

-5x^2+20x+7=0

a = -5; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·(-5)·7
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-6\sqrt{15}}{2*-5}=\frac{-20-6\sqrt{15}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+6\sqrt{15}}{2*-5}=\frac{-20+6\sqrt{15}}{-10}
$