x=x2-17/25

Solution for x=x2-17/25 equation:

x=x2-17/25

We move all terms to the left:

x-(x2-17/25)=0

We add all the numbers together, and all the variables

-(+x^2-17/25)+x=0

We get rid of parentheses

-x^2+x+17/25=0

We multiply all the terms by the denominator


-x^2*25+x*25+17=0

Wy multiply elements

-25x^2+25x+17=0

a = -25; b = 25; c = +17;
Δ = b2-4ac
Δ = 252-4·(-25)·17
Δ = 2325
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:

$\sqrt{\Delta}=\sqrt{2325}=\sqrt{25*93}=\sqrt{25}*\sqrt{93}=5\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{93}}{2*-25}=\frac{-25-5\sqrt{93}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{93}}{2*-25}=\frac{-25+5\sqrt{93}}{-50}
$