11x^2-15=1398

Solution for 11x^2-15=1398 equation:

11x^2-15=1398

We move all terms to the left:

11x^2-15-(1398)=0

We add all the numbers together, and all the variables

11x^2-1413=0

a = 11; b = 0; c = -1413;
Δ = b2-4ac
Δ = 02-4·11·(-1413)
Δ = 62172
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:

$\sqrt{\Delta}=\sqrt{62172}=\sqrt{36*1727}=\sqrt{36}*\sqrt{1727}=6\sqrt{1727}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1727}}{2*11}=\frac{0-6\sqrt{1727}}{22}
=-\frac{6\sqrt{1727}}{22}
=-\frac{3\sqrt{1727}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1727}}{2*11}=\frac{0+6\sqrt{1727}}{22}
=\frac{6\sqrt{1727}}{22}
=\frac{3\sqrt{1727}}{11}
$