5*(x-4)*(x+4)-x*(5x+7)=-143

Solution for 5*(x-4)*(x+4)-x*(5x+7)=-143 equation:

5(x-4)(x+4)-x(5x+7)=-143

We move all terms to the left:

5(x-4)(x+4)-x(5x+7)-(-143)=0

We add all the numbers together, and all the variables

5(x-4)(x+4)-x(5x+7)+143=0

We use the square of the difference formula

x^2-x(5x+7)-16+143=0

We multiply parentheses

x^2-5x^2-7x-16+143=0

We add all the numbers together, and all the variables

-4x^2-7x+127=0

a = -4; b = -7; c = +127;
Δ = b2-4ac
Δ = -72-4·(-4)·127
Δ = 2081
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{-(-7)-\sqrt{2081}}{2*-4}=\frac{7-\sqrt{2081}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{2081}}{2*-4}=\frac{7+\sqrt{2081}}{-8}
$