x2-10x=45

Solution for x2-10x=45 equation:

x2-10x=45

We move all terms to the left:

x2-10x-(45)=0

We add all the numbers together, and all the variables

x^2-10x-45=0

a = 1; b = -10; c = -45;
Δ = b2-4ac
Δ = -102-4·1·(-45)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{70}}{2*1}=\frac{10-2\sqrt{70}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{70}}{2*1}=\frac{10+2\sqrt{70}}{2}
$