x^2-77=3-2x

Solution for x^2-77=3-2x equation:

x^2-77=3-2x

We move all terms to the left:

x^2-77-(3-2x)=0

We add all the numbers together, and all the variables

x^2-(-2x+3)-77=0

We get rid of parentheses

x^2+2x-3-77=0

We add all the numbers together, and all the variables

x^2+2x-80=0

a = 1; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·1·(-80)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18}{2*1}=\frac{16}{2}
=8
$