(3x+4)(x-2)=7

Solution for (3x+4)(x-2)=7 equation:

(3x+4)(x-2)=7

We move all terms to the left:

(3x+4)(x-2)-(7)=0

We multiply parentheses ..

(+3x^2-6x+4x-8)-7=0

We get rid of parentheses

3x^2-6x+4x-8-7=0

We add all the numbers together, and all the variables

3x^2-2x-15=0

a = 3; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·3·(-15)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{46}}{2*3}=\frac{2-2\sqrt{46}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{46}}{2*3}=\frac{2+2\sqrt{46}}{6}
$