4.6x^2=54-2x

Solution for 4.6x^2=54-2x equation:

4.6x^2=54-2x

We move all terms to the left:

4.6x^2-(54-2x)=0

We add all the numbers together, and all the variables

4.6x^2-(-2x+54)=0

We get rid of parentheses

4.6x^2+2x-54=0

a = 4.6; b = 2; c = -54;
Δ = b2-4ac
Δ = 22-4·4.6·(-54)
Δ = 997.6
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{-(2)-\sqrt{997.6}}{2*4.6}=\frac{-2-\sqrt{997.6}}{9.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{997.6}}{2*4.6}=\frac{-2+\sqrt{997.6}}{9.2}
$