-2.5x^2+50x=47.5

Solution for -2.5x^2+50x=47.5 equation:

-2.5x^2+50x=47.5

We move all terms to the left:

-2.5x^2+50x-(47.5)=0

We add all the numbers together, and all the variables

-2.5x^2+50x-47.5=0

a = -2.5; b = 50; c = -47.5;
Δ = b2-4ac
Δ = 502-4·(-2.5)·(-47.5)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-45}{2*-2.5}=\frac{-95}{-5}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+45}{2*-2.5}=\frac{-5}{-5}
=1
$