x^2-45x=-4

Solution for x^2-45x=-4 equation:

x^2-45x=-4

We move all terms to the left:

x^2-45x-(-4)=0

We add all the numbers together, and all the variables

x^2-45x+4=0

a = 1; b = -45; c = +4;
Δ = b2-4ac
Δ = -452-4·1·4
Δ = 2009
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:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-7\sqrt{41}}{2*1}=\frac{45-7\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+7\sqrt{41}}{2*1}=\frac{45+7\sqrt{41}}{2}
$