49x2-4(Y+11)=3Y-2

Solution for 49x2-4(Y+11)=3Y-2 equation:

49x^2-4(+11)=3-2

We move all terms to the left:

49x^2-4(+11)-(3-2)=0

We add all the numbers together, and all the variables

49x^2-411-1=0

We add all the numbers together, and all the variables

49x^2-412=0

a = 49; b = 0; c = -412;
Δ = b2-4ac
Δ = 02-4·49·(-412)
Δ = 80752
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:

$\sqrt{\Delta}=\sqrt{80752}=\sqrt{784*103}=\sqrt{784}*\sqrt{103}=28\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{103}}{2*49}=\frac{0-28\sqrt{103}}{98}
=-\frac{28\sqrt{103}}{98}
=-\frac{2\sqrt{103}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{103}}{2*49}=\frac{0+28\sqrt{103}}{98}
=\frac{28\sqrt{103}}{98}
=\frac{2\sqrt{103}}{7}
$