3x(x+7)-5x=x+12

Solution for 3x(x+7)-5x=x+12 equation:

3x(x+7)-5x=x+12

We move all terms to the left:

3x(x+7)-5x-(x+12)=0

We add all the numbers together, and all the variables

-5x+3x(x+7)-(x+12)=0

We multiply parentheses

3x^2-5x+21x-(x+12)=0

We get rid of parentheses

3x^2-5x+21x-x-12=0

We add all the numbers together, and all the variables

3x^2+15x-12=0

a = 3; b = 15; c = -12;
Δ = b2-4ac
Δ = 152-4·3·(-12)
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{41}}{2*3}=\frac{-15-3\sqrt{41}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{41}}{2*3}=\frac{-15+3\sqrt{41}}{6}
$