7x-16=4x^2+32x

Solution for 7x-16=4x^2+32x equation:

7x-16=4x^2+32x

We move all terms to the left:

7x-16-(4x^2+32x)=0

We get rid of parentheses

-4x^2+7x-32x-16=0

We add all the numbers together, and all the variables

-4x^2-25x-16=0

a = -4; b = -25; c = -16;
Δ = b2-4ac
Δ = -252-4·(-4)·(-16)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{41}}{2*-4}=\frac{25-3\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{41}}{2*-4}=\frac{25+3\sqrt{41}}{-8}
$