49x^2-11=12

Solution for 49x^2-11=12 equation:

49x^2-11=12

We move all terms to the left:

49x^2-11-(12)=0

We add all the numbers together, and all the variables

49x^2-23=0

a = 49; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·49·(-23)
Δ = 4508
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:

$\sqrt{\Delta}=\sqrt{4508}=\sqrt{196*23}=\sqrt{196}*\sqrt{23}=14\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{23}}{2*49}=\frac{0-14\sqrt{23}}{98}
=-\frac{14\sqrt{23}}{98}
=-\frac{\sqrt{23}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{23}}{2*49}=\frac{0+14\sqrt{23}}{98}
=\frac{14\sqrt{23}}{98}
=\frac{\sqrt{23}}{7}
$