45-x*x+5x=17x

Solution for 45-x*x+5x=17x equation:

45-x*x+5x=17x

We move all terms to the left:

45-x*x+5x-(17x)=0

We add all the numbers together, and all the variables

-12x-x*x+45=0

Wy multiply elements

-1x^2-12x+45=0

a = -1; b = -12; c = +45;
Δ = b2-4ac
Δ = -122-4·(-1)·45
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*-1}=\frac{30}{-2}
=-15
$