-7x(x+5)-41=4-24

Solution for -7x(x+5)-41=4-24 equation:

-7x(x+5)-41=4-24

We move all terms to the left:

-7x(x+5)-41-(4-24)=0

We add all the numbers together, and all the variables

-7x(x+5)-41-(-20)=0

We add all the numbers together, and all the variables

-7x(x+5)-21=0

We multiply parentheses

-7x^2-35x-21=0

a = -7; b = -35; c = -21;
Δ = b2-4ac
Δ = -352-4·(-7)·(-21)
Δ = 637
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:

$\sqrt{\Delta}=\sqrt{637}=\sqrt{49*13}=\sqrt{49}*\sqrt{13}=7\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-7\sqrt{13}}{2*-7}=\frac{35-7\sqrt{13}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+7\sqrt{13}}{2*-7}=\frac{35+7\sqrt{13}}{-14}
$