X(6x+5)=7x+5x

Solution for X(6x+5)=7x+5x equation:

X(6X+5)=7X+5X

We move all terms to the left:

X(6X+5)-(7X+5X)=0

We add all the numbers together, and all the variables

X(6X+5)-(+12X)=0

We multiply parentheses

6X^2+5X-(+12X)=0

We get rid of parentheses

6X^2+5X-12X=0

We add all the numbers together, and all the variables

6X^2-7X=0

a = 6; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·6·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*6}=\frac{0}{12}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*6}=\frac{14}{12}
=1+1/6
$