X(6x+5)=12x+10

Solution for X(6x+5)=12x+10 equation:

X(6X+5)=12X+10

We move all terms to the left:

X(6X+5)-(12X+10)=0

We multiply parentheses

6X^2+5X-(12X+10)=0

We get rid of parentheses

6X^2+5X-12X-10=0

We add all the numbers together, and all the variables

6X^2-7X-10=0

a = 6; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·6·(-10)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*6}=\frac{-10}{12}
=-5/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*6}=\frac{24}{12}
=2
$