-3x^2-7x=16x-54

Solution for -3x^2-7x=16x-54 equation:

-3x^2-7x=16x-54

We move all terms to the left:

-3x^2-7x-(16x-54)=0

We get rid of parentheses

-3x^2-7x-16x+54=0

We add all the numbers together, and all the variables

-3x^2-23x+54=0

a = -3; b = -23; c = +54;
Δ = b2-4ac
Δ = -232-4·(-3)·54
Δ = 1177
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{-(-23)-\sqrt{1177}}{2*-3}=\frac{23-\sqrt{1177}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1177}}{2*-3}=\frac{23+\sqrt{1177}}{-6}
$