5.57=35-24x+4x^2

Solution for 5.57=35-24x+4x^2 equation:

5.57=35-24x+4x^2

We move all terms to the left:

5.57-(35-24x+4x^2)=0

We get rid of parentheses

-4x^2+24x-35+5.57=0

We add all the numbers together, and all the variables

-4x^2+24x-29.43=0

a = -4; b = 24; c = -29.43;
Δ = b2-4ac
Δ = 242-4·(-4)·(-29.43)
Δ = 105.12
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{-(24)-\sqrt{105.12}}{2*-4}=\frac{-24-\sqrt{105.12}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+\sqrt{105.12}}{2*-4}=\frac{-24+\sqrt{105.12}}{-8}
$