(3x-7)(x+4)=10

Solution for (3x-7)(x+4)=10 equation:

(3x-7)(x+4)=10

We move all terms to the left:

(3x-7)(x+4)-(10)=0

We multiply parentheses ..

(+3x^2+12x-7x-28)-10=0

We get rid of parentheses

3x^2+12x-7x-28-10=0

We add all the numbers together, and all the variables

3x^2+5x-38=0

a = 3; b = 5; c = -38;
Δ = b2-4ac
Δ = 52-4·3·(-38)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{481}}{2*3}=\frac{-5-\sqrt{481}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{481}}{2*3}=\frac{-5+\sqrt{481}}{6}
$