10/3=x^2-x

Solution for 10/3=x^2-x equation:

10/3=x^2-x

We move all terms to the left:

10/3-(x^2-x)=0

We get rid of parentheses

-x^2+x+10/3=0

We multiply all the terms by the denominator


-x^2*3+x*3+10=0

Wy multiply elements

-3x^2+3x+10=0

a = -3; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-3)·10
Δ = 129
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{-(3)-\sqrt{129}}{2*-3}=\frac{-3-\sqrt{129}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{129}}{2*-3}=\frac{-3+\sqrt{129}}{-6}
$