-x^2+15x=13-3x

Solution for -x^2+15x=13-3x equation:

-x^2+15x=13-3x

We move all terms to the left:

-x^2+15x-(13-3x)=0

We add all the numbers together, and all the variables

-x^2+15x-(-3x+13)=0

We add all the numbers together, and all the variables

-1x^2+15x-(-3x+13)=0

We get rid of parentheses

-1x^2+15x+3x-13=0

We add all the numbers together, and all the variables

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

a = -1; b = 18; c = -13;
Δ = b2-4ac
Δ = 182-4·(-1)·(-13)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{17}}{2*-1}=\frac{-18-4\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{17}}{2*-1}=\frac{-18+4\sqrt{17}}{-2}
$