13x^2-16x=x^2-x

Solution for 13x^2-16x=x^2-x equation:

13x^2-16x=x^2-x

We move all terms to the left:

13x^2-16x-(x^2-x)=0

We get rid of parentheses

13x^2-x^2-16x+x=0

We add all the numbers together, and all the variables

12x^2-15x=0

a = 12; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·12·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*12}=\frac{30}{24}
=1+1/4
$