4/5x-17=34,x

Solution for 4/5x-17=34,x equation:

4/5x-17=34.x

We move all terms to the left:

4/5x-17-(34.x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(+34.x)-17=0

We get rid of parentheses

4/5x-34.x-17=0

We multiply all the terms by the denominator


-(34.x)*5x-17*5x+4=0

We add all the numbers together, and all the variables

-(+34.x)*5x-17*5x+4=0

We multiply parentheses

-170x^2-17*5x+4=0

Wy multiply elements

-170x^2-85x+4=0

a = -170; b = -85; c = +4;
Δ = b2-4ac
Δ = -852-4·(-170)·4
Δ = 9945
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:

$\sqrt{\Delta}=\sqrt{9945}=\sqrt{9*1105}=\sqrt{9}*\sqrt{1105}=3\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-3\sqrt{1105}}{2*-170}=\frac{85-3\sqrt{1105}}{-340}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+3\sqrt{1105}}{2*-170}=\frac{85+3\sqrt{1105}}{-340}
$