54.3x^2-(11.5*54.3)x+(33.0625*54.3)-(4x^2)=0

Solution for 54.3x^2-(11.5*54.3)x+(33.0625*54.3)-(4x^2)=0 equation:

54.3x^2-(11.5*54.3)x+(33.0625*54.3)-(4x^2)=0

determiningTheFunctionDomain
54.3x^2-4x^2-(11.5*54.3)x+(33.0625*54.3)=0

We add all the numbers together, and all the variables

54.3x^2-4x^2-(624.45)x+(1795.29375)=0

We add all the numbers together, and all the variables

50.3x^2-(624.45)x+1795.29375=0

We multiply parentheses

50.3x^2-624.45x+1795.29375=0

a = 50.3; b = -624.45; c = +1795.29375;
Δ = b2-4ac
Δ = -624.452-4·50.3·1795.29375
Δ = 28724.7
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{-(-624.45)-\sqrt{28724.7}}{2*50.3}=\frac{624.45-\sqrt{28724.7}}{100.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-624.45)+\sqrt{28724.7}}{2*50.3}=\frac{624.45+\sqrt{28724.7}}{100.6}
$