-6x^2+9x-1=-18x+13

Solution for -6x^2+9x-1=-18x+13 equation:

-6x^2+9x-1=-18x+13

We move all terms to the left:

-6x^2+9x-1-(-18x+13)=0

We get rid of parentheses

-6x^2+9x+18x-13-1=0

We add all the numbers together, and all the variables

-6x^2+27x-14=0

a = -6; b = 27; c = -14;
Δ = b2-4ac
Δ = 272-4·(-6)·(-14)
Δ = 393
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{-(27)-\sqrt{393}}{2*-6}=\frac{-27-\sqrt{393}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{393}}{2*-6}=\frac{-27+\sqrt{393}}{-12}
$