6y*3y+43=180

Solution for 6y*3y+43=180 equation:

6y*3y+43=180

We move all terms to the left:

6y*3y+43-(180)=0

We add all the numbers together, and all the variables

6y*3y-137=0

Wy multiply elements

18y^2-137=0

a = 18; b = 0; c = -137;
Δ = b2-4ac
Δ = 02-4·18·(-137)
Δ = 9864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9864}=\sqrt{36*274}=\sqrt{36}*\sqrt{274}=6\sqrt{274}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{274}}{2*18}=\frac{0-6\sqrt{274}}{36}
=-\frac{6\sqrt{274}}{36}
=-\frac{\sqrt{274}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{274}}{2*18}=\frac{0+6\sqrt{274}}{36}
=\frac{6\sqrt{274}}{36}
=\frac{\sqrt{274}}{6}
$