4x^2-54x=-176

Solution for 4x^2-54x=-176 equation:

4x^2-54x=-176

We move all terms to the left:

4x^2-54x-(-176)=0

We add all the numbers together, and all the variables

4x^2-54x+176=0

a = 4; b = -54; c = +176;
Δ = b2-4ac
Δ = -542-4·4·176
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-10}{2*4}=\frac{44}{8}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+10}{2*4}=\frac{64}{8}
=8
$