57x=-7x^2+54

Solution for 57x=-7x^2+54 equation:

57x=-7x^2+54

We move all terms to the left:

57x-(-7x^2+54)=0

We get rid of parentheses

7x^2+57x-54=0

a = 7; b = 57; c = -54;
Δ = b2-4ac
Δ = 572-4·7·(-54)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-69}{2*7}=\frac{-126}{14}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+69}{2*7}=\frac{12}{14}
=6/7
$