4x^2+80x=106.25

Solution for 4x^2+80x=106.25 equation:

4x^2+80x=106.25

We move all terms to the left:

4x^2+80x-(106.25)=0

We add all the numbers together, and all the variables

4x^2+80x-106.25=0

a = 4; b = 80; c = -106.25;
Δ = b2-4ac
Δ = 802-4·4·(-106.25)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-90}{2*4}=\frac{-170}{8}
=-21+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+90}{2*4}=\frac{10}{8}
=1+1/4
$