(4x-55)x=20

Solution for (4x-55)x=20 equation:

(4x-55)x=20

We move all terms to the left:

(4x-55)x-(20)=0

We multiply parentheses

4x^2-55x-20=0

a = 4; b = -55; c = -20;
Δ = b2-4ac
Δ = -552-4·4·(-20)
Δ = 3345
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{-(-55)-\sqrt{3345}}{2*4}=\frac{55-\sqrt{3345}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3345}}{2*4}=\frac{55+\sqrt{3345}}{8}
$