59-34=x^2-x

Solution for 59-34=x^2-x equation:

59-34=x^2-x

We move all terms to the left:

59-34-(x^2-x)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+x+25=0

We add all the numbers together, and all the variables

-1x^2+x+25=0

a = -1; b = 1; c = +25;
Δ = b2-4ac
Δ = 12-4·(-1)·25
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{101}}{2*-1}=\frac{-1-\sqrt{101}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{101}}{2*-1}=\frac{-1+\sqrt{101}}{-2}
$