-37-11x=5x-3x2-2

Solution for -37-11x=5x-3x2-2 equation:

-37-11x=5x-3x^2-2

We move all terms to the left:

-37-11x-(5x-3x^2-2)=0

We get rid of parentheses

3x^2-5x-11x+2-37=0

We add all the numbers together, and all the variables

3x^2-16x-35=0

a = 3; b = -16; c = -35;
Δ = b2-4ac
Δ = -162-4·3·(-35)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-26}{2*3}=\frac{-10}{6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+26}{2*3}=\frac{42}{6}
=7
$