(3x+2)(x-5)=28-3x

Solution for (3x+2)(x-5)=28-3x equation:

(3x+2)(x-5)=28-3x

We move all terms to the left:

(3x+2)(x-5)-(28-3x)=0

We add all the numbers together, and all the variables

(3x+2)(x-5)-(-3x+28)=0

We get rid of parentheses

(3x+2)(x-5)+3x-28=0

We multiply parentheses ..

(+3x^2-15x+2x-10)+3x-28=0

We get rid of parentheses

3x^2-15x+2x+3x-10-28=0

We add all the numbers together, and all the variables

3x^2-10x-38=0

a = 3; b = -10; c = -38;
Δ = b2-4ac
Δ = -102-4·3·(-38)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{139}}{2*3}=\frac{10-2\sqrt{139}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{139}}{2*3}=\frac{10+2\sqrt{139}}{6}
$