25-1+7y+4(y+4)=-5(5y-3)-8(y+1)21y+10

Solution for 25-1+7y+4(y+4)=-5(5y-3)-8(y+1)21y+10 equation:

25-1+7y+4(y+4)=-5(5y-3)-8(y+1)21y+10

We move all terms to the left:

25-1+7y+4(y+4)-(-5(5y-3)-8(y+1)21y+10)=0

We add all the numbers together, and all the variables

7y+4(y+4)-(-5(5y-3)-8(y+1)21y+10)+24=0

We multiply parentheses

7y+4y-(-5(5y-3)-8(y+1)21y+10)+16+24=0


We calculate terms in parentheses: -(-5(5y-3)-8(y+1)21y+10), so:

-5(5y-3)-8(y+1)21y+10

We multiply parentheses

-168y^2-25y-168y+15+10

We add all the numbers together, and all the variables

-168y^2-193y+25

Back to the equation:

-(-168y^2-193y+25)


We add all the numbers together, and all the variables

-(-168y^2-193y+25)+11y+40=0

We get rid of parentheses

168y^2+193y+11y-25+40=0

We add all the numbers together, and all the variables

168y^2+204y+15=0

a = 168; b = 204; c = +15;
Δ = b2-4ac
Δ = 2042-4·168·15
Δ = 31536
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:

$\sqrt{\Delta}=\sqrt{31536}=\sqrt{144*219}=\sqrt{144}*\sqrt{219}=12\sqrt{219}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(204)-12\sqrt{219}}{2*168}=\frac{-204-12\sqrt{219}}{336}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(204)+12\sqrt{219}}{2*168}=\frac{-204+12\sqrt{219}}{336}
$