4.1x(x-2.7)=254.2

Solution for 4.1x(x-2.7)=254.2 equation:

4.1x(x-2.7)=254.2

We move all terms to the left:

4.1x(x-2.7)-(254.2)=0

We add all the numbers together, and all the variables

4.1x(x-2.7)-254.2=0

We multiply parentheses

4x^2-10.8x-254.2=0

a = 4; b = -10.8; c = -254.2;
Δ = b2-4ac
Δ = -10.82-4·4·(-254.2)
Δ = 4183.84
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{-(-10.8)-\sqrt{4183.84}}{2*4}=\frac{10.8-\sqrt{4183.84}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.8)+\sqrt{4183.84}}{2*4}=\frac{10.8+\sqrt{4183.84}}{8}
$