-4x(x+3)+57=-35

Solution for -4x(x+3)+57=-35 equation:

-4x(x+3)+57=-35

We move all terms to the left:

-4x(x+3)+57-(-35)=0

We add all the numbers together, and all the variables

-4x(x+3)+92=0

We multiply parentheses

-4x^2-12x+92=0

a = -4; b = -12; c = +92;
Δ = b2-4ac
Δ = -122-4·(-4)·92
Δ = 1616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{101}}{2*-4}=\frac{12-4\sqrt{101}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{101}}{2*-4}=\frac{12+4\sqrt{101}}{-8}
$