17/5x-4x=-2=-2x+21/20

Solution for 17/5x-4x=-2=-2x+21/20 equation:

17/5x-4x=-2=-2x+21/20

We move all terms to the left:

17/5x-4x-(-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+17/5x+2=0

We multiply all the terms by the denominator


-4x*5x+2*5x+17=0

Wy multiply elements

-20x^2+10x+17=0

a = -20; b = 10; c = +17;
Δ = b2-4ac
Δ = 102-4·(-20)·17
Δ = 1460
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:

$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{365}}{2*-20}=\frac{-10-2\sqrt{365}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{365}}{2*-20}=\frac{-10+2\sqrt{365}}{-40}
$