-5w^2+22w=-48

Solution for -5w^2+22w=-48 equation:

-5w^2+22w=-48

We move all terms to the left:

-5w^2+22w-(-48)=0

We add all the numbers together, and all the variables

-5w^2+22w+48=0

a = -5; b = 22; c = +48;
Δ = b2-4ac
Δ = 222-4·(-5)·48
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-38}{2*-5}=\frac{-60}{-10}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+38}{2*-5}=\frac{16}{-10}
=-1+3/5
$