-3(2y+3)-17=-4(y+8)2y

Solution for -3(2y+3)-17=-4(y+8)2y equation:

-3(2y+3)-17=-4(y+8)2y

We move all terms to the left:

-3(2y+3)-17-(-4(y+8)2y)=0

We multiply parentheses

-6y-(-4(y+8)2y)-9-17=0


We calculate terms in parentheses: -(-4(y+8)2y), so:

-4(y+8)2y

We multiply parentheses

-8y^2-64y

Back to the equation:

-(-8y^2-64y)


We add all the numbers together, and all the variables

-(-8y^2-64y)-6y-26=0

We get rid of parentheses

8y^2+64y-6y-26=0

We add all the numbers together, and all the variables

8y^2+58y-26=0

a = 8; b = 58; c = -26;
Δ = b2-4ac
Δ = 582-4·8·(-26)
Δ = 4196
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:

$\sqrt{\Delta}=\sqrt{4196}=\sqrt{4*1049}=\sqrt{4}*\sqrt{1049}=2\sqrt{1049}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{1049}}{2*8}=\frac{-58-2\sqrt{1049}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{1049}}{2*8}=\frac{-58+2\sqrt{1049}}{16}
$