X.3(x-5)=12+2x

Solution for X.3(x-5)=12+2x equation:

X.3(X-5)=12+2X

We move all terms to the left:

X.3(X-5)-(12+2X)=0

We add all the numbers together, and all the variables

X.3(X-5)-(2X+12)=0

We multiply parentheses

X^2-5X-(2X+12)=0

We get rid of parentheses

X^2-5X-2X-12=0

We add all the numbers together, and all the variables

X^2-7X-12=0

a = 1; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·1·(-12)
Δ = 97
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{-(-7)-\sqrt{97}}{2*1}=\frac{7-\sqrt{97}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*1}=\frac{7+\sqrt{97}}{2}
$