20x^2-80x=45

Solution for 20x^2-80x=45 equation:

20x^2-80x=45

We move all terms to the left:

20x^2-80x-(45)=0

a = 20; b = -80; c = -45;
Δ = b2-4ac
Δ = -802-4·20·(-45)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-100}{2*20}=\frac{-20}{40}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+100}{2*20}=\frac{180}{40}
=4+1/2
$