3x(x+7)=23-3x+2

Solution for 3x(x+7)=23-3x+2 equation:

3x(x+7)=23-3x+2

We move all terms to the left:

3x(x+7)-(23-3x+2)=0

We add all the numbers together, and all the variables

3x(x+7)-(-3x+25)=0

We multiply parentheses

3x^2+21x-(-3x+25)=0

We get rid of parentheses

3x^2+21x+3x-25=0

We add all the numbers together, and all the variables

3x^2+24x-25=0

a = 3; b = 24; c = -25;
Δ = b2-4ac
Δ = 242-4·3·(-25)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{219}}{2*3}=\frac{-24-2\sqrt{219}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{219}}{2*3}=\frac{-24+2\sqrt{219}}{6}
$