(X-1)(2x+5(3-x))=0

Solution for (X-1)(2x+5(3-x))=0 equation:

(X-1)(2X+5(3-X))=0

We add all the numbers together, and all the variables

(X-1)(2X+5(-1X+3))=0


We calculate terms in parentheses: +(X-1)(2X+5(-1X+3)), so:

X-1)(2X+5(-1X+3)

We multiply parentheses

X-1)(2X-5X+15

We add all the numbers together, and all the variables

-4X-1)(2X+15

Back to the equation:

+(-4X-1)(2X+15)


We multiply parentheses ..

(-8X^2-60X-2X-15)=0

We get rid of parentheses

-8X^2-60X-2X-15=0

We add all the numbers together, and all the variables

-8X^2-62X-15=0

a = -8; b = -62; c = -15;
Δ = b2-4ac
Δ = -622-4·(-8)·(-15)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-58}{2*-8}=\frac{4}{-16}
=-1/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+58}{2*-8}=\frac{120}{-16}
=-7+1/2
$