-41x^2=-44032

Solution for -41x^2=-44032 equation:

-41x^2=-44032

We move all terms to the left:

-41x^2-(-44032)=0

We add all the numbers together, and all the variables

-41x^2+44032=0

a = -41; b = 0; c = +44032;
Δ = b2-4ac
Δ = 02-4·(-41)·44032
Δ = 7221248
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:

$\sqrt{\Delta}=\sqrt{7221248}=\sqrt{4096*1763}=\sqrt{4096}*\sqrt{1763}=64\sqrt{1763}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{1763}}{2*-41}=\frac{0-64\sqrt{1763}}{-82}
=-\frac{64\sqrt{1763}}{-82}
=-\frac{32\sqrt{1763}}{-41}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{1763}}{2*-41}=\frac{0+64\sqrt{1763}}{-82}
=\frac{64\sqrt{1763}}{-82}
=\frac{32\sqrt{1763}}{-41}
$