A4-7a2=-11

Solution for A4-7a2=-11 equation:

4-7A^2=-11

We move all terms to the left:

4-7A^2-(-11)=0

We add all the numbers together, and all the variables

-7A^2+15=0

a = -7; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-7)·15
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*-7}=\frac{0-2\sqrt{105}}{-14}
=-\frac{2\sqrt{105}}{-14}
=-\frac{\sqrt{105}}{-7}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*-7}=\frac{0+2\sqrt{105}}{-14}
=\frac{2\sqrt{105}}{-14}
=\frac{\sqrt{105}}{-7}
$