-x^2+9x=4x-12

Solution for -x^2+9x=4x-12 equation:

-x^2+9x=4x-12

We move all terms to the left:

-x^2+9x-(4x-12)=0

We add all the numbers together, and all the variables

-1x^2+9x-(4x-12)=0

We get rid of parentheses

-1x^2+9x-4x+12=0

We add all the numbers together, and all the variables

-1x^2+5x+12=0

a = -1; b = 5; c = +12;
Δ = b2-4ac
Δ = 52-4·(-1)·12
Δ = 73
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{-(5)-\sqrt{73}}{2*-1}=\frac{-5-\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*-1}=\frac{-5+\sqrt{73}}{-2}
$