1/2(3y)=11y-20

Solution for 1/2(3y)=11y-20 equation:

1/2(3y)=11y-20

We move all terms to the left:

1/2(3y)-(11y-20)=0


Domain of the equation: 23y!=0

y!=0/23

y!=0

y∈R


We get rid of parentheses

1/23y-11y+20=0

We multiply all the terms by the denominator


-11y*23y+20*23y+1=0

Wy multiply elements

-253y^2+460y+1=0

a = -253; b = 460; c = +1;
Δ = b2-4ac
Δ = 4602-4·(-253)·1
Δ = 212612
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:

$\sqrt{\Delta}=\sqrt{212612}=\sqrt{4*53153}=\sqrt{4}*\sqrt{53153}=2\sqrt{53153}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(460)-2\sqrt{53153}}{2*-253}=\frac{-460-2\sqrt{53153}}{-506}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(460)+2\sqrt{53153}}{2*-253}=\frac{-460+2\sqrt{53153}}{-506}
$