43.125=x^2-19x

Solution for 43.125=x^2-19x equation:

43.125=x^2-19x

We move all terms to the left:

43.125-(x^2-19x)=0

We get rid of parentheses

-x^2+19x+43.125=0

We add all the numbers together, and all the variables

-1x^2+19x+43.125=0

a = -1; b = 19; c = +43.125;
Δ = b2-4ac
Δ = 192-4·(-1)·43.125
Δ = 533.5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{533.5}}{2*-1}=\frac{-19-\sqrt{533.5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{533.5}}{2*-1}=\frac{-19+\sqrt{533.5}}{-2}
$