4x^2=19.188-63.69x+53.3x^2

Solution for 4x^2=19.188-63.69x+53.3x^2 equation:

4x^2=19.188-63.69x+53.3x^2

We move all terms to the left:

4x^2-(19.188-63.69x+53.3x^2)=0

We get rid of parentheses

4x^2-53.3x^2+63.69x-19.188=0

We add all the numbers together, and all the variables

-49.3x^2+63.69x-19.188=0

a = -49.3; b = 63.69; c = -19.188;
Δ = b2-4ac
Δ = 63.692-4·(-49.3)·(-19.188)
Δ = 272.5425
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{-(63.69)-\sqrt{272.5425}}{2*-49.3}=\frac{-63.69-\sqrt{272.5425}}{-98.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63.69)+\sqrt{272.5425}}{2*-49.3}=\frac{-63.69+\sqrt{272.5425}}{-98.6}
$