2x(x-16)+7x=40

Solution for 2x(x-16)+7x=40 equation:

2x(x-16)+7x=40

We move all terms to the left:

2x(x-16)+7x-(40)=0

We add all the numbers together, and all the variables

7x+2x(x-16)-40=0

We multiply parentheses

2x^2+7x-32x-40=0

We add all the numbers together, and all the variables

2x^2-25x-40=0

a = 2; b = -25; c = -40;
Δ = b2-4ac
Δ = -252-4·2·(-40)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{105}}{2*2}=\frac{25-3\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{105}}{2*2}=\frac{25+3\sqrt{105}}{4}
$