(-17/31)x+7/41=(15/31)

Solution for (-17/31)x+7/41=(15/31) equation:

(-17/31)x+7/41=(15/31)

We move all terms to the left:

(-17/31)x+7/41-((15/31))=0


Domain of the equation: 31)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-17/31)x+7/41-((+15/31))=0

We multiply parentheses

-17x^2+7/41-((+15/31))=0

We calculate fractions


-17x^2+()/()+()/()=0

We add all the numbers together, and all the variables

-17x^2+2=0

a = -17; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-17)·2
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{34}}{2*-17}=\frac{0-2\sqrt{34}}{-34}
=-\frac{2\sqrt{34}}{-34}
=-\frac{\sqrt{34}}{-17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{34}}{2*-17}=\frac{0+2\sqrt{34}}{-34}
=\frac{2\sqrt{34}}{-34}
=\frac{\sqrt{34}}{-17}
$