X(3x+10)=8(x+2)

Solution for X(3x+10)=8(x+2) equation:

X(3X+10)=8(X+2)

We move all terms to the left:

X(3X+10)-(8(X+2))=0

We multiply parentheses

3X^2+10X-(8(X+2))=0


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

8(X+2)

We multiply parentheses

8X+16

Back to the equation:

-(8X+16)


We get rid of parentheses

3X^2+10X-8X-16=0

We add all the numbers together, and all the variables

3X^2+2X-16=0

a = 3; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·3·(-16)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*3}=\frac{-16}{6}
=-2+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*3}=\frac{12}{6}
=2
$