x^2-4x-77+x=-67-3x

Solution for x^2-4x-77+x=-67-3x equation:

x^2-4x-77+x=-67-3x

We move all terms to the left:

x^2-4x-77+x-(-67-3x)=0

We add all the numbers together, and all the variables

x^2-4x+x-(-3x-67)-77=0

We add all the numbers together, and all the variables

x^2-3x-(-3x-67)-77=0

We get rid of parentheses

x^2-3x+3x+67-77=0

We add all the numbers together, and all the variables

x^2-10=0

a = 1; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·1·(-10)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*1}=\frac{0-2\sqrt{10}}{2}
=-\frac{2\sqrt{10}}{2}
=-\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*1}=\frac{0+2\sqrt{10}}{2}
=\frac{2\sqrt{10}}{2}
=\sqrt{10}
$