X+258=(x+6)(x+10)

Solution for X+258=(x+6)(x+10) equation:

X+258=(X+6)(X+10)

We move all terms to the left:

X+258-((X+6)(X+10))=0

We multiply parentheses ..

-((+X^2+10X+6X+60))+X+258=0


We calculate terms in parentheses: -((+X^2+10X+6X+60)), so:

(+X^2+10X+6X+60)

We get rid of parentheses

X^2+10X+6X+60

We add all the numbers together, and all the variables

X^2+16X+60

Back to the equation:

-(X^2+16X+60)


We add all the numbers together, and all the variables

X-(X^2+16X+60)+258=0

We get rid of parentheses

-X^2+X-16X-60+258=0

We add all the numbers together, and all the variables

-1X^2-15X+198=0

a = -1; b = -15; c = +198;
Δ = b2-4ac
Δ = -152-4·(-1)·198
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{113}}{2*-1}=\frac{15-3\sqrt{113}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{113}}{2*-1}=\frac{15+3\sqrt{113}}{-2}
$