x+3/5x+6x-25/5=569

Solution for x+3/5x+6x-25/5=569 equation:

x+3/5x+6x-25/5=569

We move all terms to the left:

x+3/5x+6x-25/5-(569)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


determiningTheFunctionDomain
x+3/5x+6x-569-25/5=0

We add all the numbers together, and all the variables

7x+3/5x-574=0

We multiply all the terms by the denominator


7x*5x-574*5x+3=0

Wy multiply elements

35x^2-2870x+3=0

a = 35; b = -2870; c = +3;
Δ = b2-4ac
Δ = -28702-4·35·3
Δ = 8236480
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:

$\sqrt{\Delta}=\sqrt{8236480}=\sqrt{64*128695}=\sqrt{64}*\sqrt{128695}=8\sqrt{128695}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2870)-8\sqrt{128695}}{2*35}=\frac{2870-8\sqrt{128695}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2870)+8\sqrt{128695}}{2*35}=\frac{2870+8\sqrt{128695}}{70}
$