45-34-2y-41y+724=-411+3y2-34-31y+22-212y-524

Solution for 45-34-2y-41y+724=-411+3y2-34-31y+22-212y-524 equation:

45-34-2y-41y+724=-411+3y^2-34-31y+22-212y-524

We move all terms to the left:

45-34-2y-41y+724-(-411+3y^2-34-31y+22-212y-524)=0

We add all the numbers together, and all the variables

-(-411+3y^2-34-31y+22-212y-524)-43y+735=0

We get rid of parentheses

-3y^2+31y+212y-43y+411+34-22+524+735=0

We add all the numbers together, and all the variables

-3y^2+200y+1682=0

a = -3; b = 200; c = +1682;
Δ = b2-4ac
Δ = 2002-4·(-3)·1682
Δ = 60184
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:

$\sqrt{\Delta}=\sqrt{60184}=\sqrt{4*15046}=\sqrt{4}*\sqrt{15046}=2\sqrt{15046}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{15046}}{2*-3}=\frac{-200-2\sqrt{15046}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{15046}}{2*-3}=\frac{-200+2\sqrt{15046}}{-6}
$