88=(x(x-15))+(x)+(x-2)

Solution for 88=(x(x-15))+(x)+(x-2) equation:

88=(x(x-15))+(x)+(x-2)

We move all terms to the left:

88-((x(x-15))+(x)+(x-2))=0


We calculate terms in parentheses: -((x(x-15))+x+(x-2)), so:

(x(x-15))+x+(x-2)

We add all the numbers together, and all the variables

x+(x(x-15))+(x-2)

We get rid of parentheses

x+(x(x-15))+x-2


We calculate terms in parentheses: +(x(x-15)), so:

x(x-15)

We multiply parentheses

x^2-15x

Back to the equation:

+(x^2-15x)


We add all the numbers together, and all the variables

2x+(x^2-15x)-2

We get rid of parentheses

x^2+2x-15x-2

We add all the numbers together, and all the variables

x^2-13x-2

Back to the equation:

-(x^2-13x-2)


We get rid of parentheses

-x^2+13x+2+88=0

We add all the numbers together, and all the variables

-1x^2+13x+90=0

a = -1; b = 13; c = +90;
Δ = b2-4ac
Δ = 132-4·(-1)·90
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*-1}=\frac{10}{-2}
=-5
$