3X2+2y2-143=54y

Solution for 3X2+2y2-143=54y equation:

3X^2+2X^2-143=54X

We move all terms to the left:

3X^2+2X^2-143-(54X)=0

We add all the numbers together, and all the variables

5X^2-54X-143=0

a = 5; b = -54; c = -143;
Δ = b2-4ac
Δ = -542-4·5·(-143)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-76}{2*5}=\frac{-22}{10}
=-2+1/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+76}{2*5}=\frac{130}{10}
=13
$