3x-5=(x*x)-2x-8

Solution for 3x-5=(x*x)-2x-8 equation:

3x-5=(x*x)-2x-8

We move all terms to the left:

3x-5-((x*x)-2x-8)=0

We add all the numbers together, and all the variables

3x-((+x*x)-2x-8)-5=0


We calculate terms in parentheses: -((+x*x)-2x-8), so:

(+x*x)-2x-8

We add all the numbers together, and all the variables

-2x+(+x*x)-8

We get rid of parentheses

-2x+x*x-8

Wy multiply elements

x^2-2x-8

Back to the equation:

-(x^2-2x-8)


We get rid of parentheses

-x^2+3x+2x+8-5=0

We add all the numbers together, and all the variables

-1x^2+5x+3=0

a = -1; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-1)·3
Δ = 37
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{-(5)-\sqrt{37}}{2*-1}=\frac{-5-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-1}=\frac{-5+\sqrt{37}}{-2}
$