-1-4r^2=-357

Solution for -1-4r^2=-357 equation:

-1-4r^2=-357

We move all terms to the left:

-1-4r^2-(-357)=0

We add all the numbers together, and all the variables

-4r^2+356=0

a = -4; b = 0; c = +356;
Δ = b2-4ac
Δ = 02-4·(-4)·356
Δ = 5696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{89}}{2*-4}=\frac{0-8\sqrt{89}}{-8}
=-\frac{8\sqrt{89}}{-8}
=-\frac{\sqrt{89}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{89}}{2*-4}=\frac{0+8\sqrt{89}}{-8}
=\frac{8\sqrt{89}}{-8}
=\frac{\sqrt{89}}{-1}
$