2y(y+9)=3(y+9)

Simple and best practice solution for 2y(y+9)=3(y+9) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 2y(y+9)=3(y+9) equation:



2y(y+9)=3(y+9)
We move all terms to the left:
2y(y+9)-(3(y+9))=0
We multiply parentheses
2y^2+18y-(3(y+9))=0
We calculate terms in parentheses: -(3(y+9)), so:
3(y+9)
We multiply parentheses
3y+27
Back to the equation:
-(3y+27)
We get rid of parentheses
2y^2+18y-3y-27=0
We add all the numbers together, and all the variables
2y^2+15y-27=0
a = 2; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·2·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*2}=\frac{-36}{4} =-9 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*2}=\frac{6}{4} =1+1/2 $

See similar equations:

| 1/4x+1/8x=5 | | 375+125h=250+175h | | -31+3k=-14k+18 | | -16t^2+384t+4=0 | | 3x=5x+-4 | | 7a+10=2a+15 | | .666k+9=5 | | -8-3k=-8(1-8k | | 1/2j-16=2/3j-14 | | -5(k+8)=-31-2k | | x+3/3=3(x-7) | | 6×x+4=x-11 | | 24-(3x)=-27 | | 32+b=-(-8b-8)-4b | | A-32=-3(4-2a) | | 24-(3x)=3 | | 1/2(16-x)=11/2x | | A4=a4-1+3 | | 2/x=20/15 | | 212=5x+3(8x+3) | | 4×x-5=2x×3 | | d3.03=2 | | 12=6(x-4) | | 7t-2t-2=13 | | -0.8x=8 | | 14x^2-67x=-6 | | 5x+3x+10=2(4x+5) | | 1/2(16-i)=11/2 | | 3(5-n)=2n-10 | | 3(x+4)=-2(1.5x-6) | | 4+1x=1 | | 2(x=8)=x+19 |

Equations solver categories