-x^2=35+12x

Solution for -x^2=35+12x equation:

-x^2=35+12x

We move all terms to the left:

-x^2-(35+12x)=0

We add all the numbers together, and all the variables

-x^2-(12x+35)=0

We add all the numbers together, and all the variables

-1x^2-(12x+35)=0

We get rid of parentheses

-1x^2-12x-35=0

a = -1; b = -12; c = -35;
Δ = b2-4ac
Δ = -122-4·(-1)·(-35)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*-1}=\frac{10}{-2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*-1}=\frac{14}{-2}
=-7
$