x2+5x-104=3(x-8)

Solution for x2+5x-104=3(x-8) equation:

x2+5x-104=3(x-8)

We move all terms to the left:

x2+5x-104-(3(x-8))=0

We add all the numbers together, and all the variables

x^2+5x-(3(x-8))-104=0


We calculate terms in parentheses: -(3(x-8)), so:

3(x-8)

We multiply parentheses

3x-24

Back to the equation:

-(3x-24)


We get rid of parentheses

x^2+5x-3x+24-104=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
$