7(y-8)+24=(4/7)(y-6)

Solution for 7(y-8)+24=(4/7)(y-6) equation:

7(y-8)+24=(4/7)(y-6)

We move all terms to the left:

7(y-8)+24-((4/7)(y-6))=0


Domain of the equation: 7)(y-6))!=0

y∈R


We add all the numbers together, and all the variables

7(y-8)-((+4/7)(y-6))+24=0

We multiply parentheses

7y-((+4/7)(y-6))-56+24=0

We multiply parentheses ..

-((+4y^2+4/7*-6))+7y-56+24=0

We multiply all the terms by the denominator


-((+4y^2+4+7y*7*-6))-56*7*-6))+24*7*-6))=0


We calculate terms in parentheses: -((+4y^2+4+7y*7*-6)), so:

(+4y^2+4+7y*7*-6)

We get rid of parentheses

4y^2+7y*7*+4-6

We add all the numbers together, and all the variables

4y^2+7y*7*-2

Wy multiply elements

4y^2+49y^2-2

We add all the numbers together, and all the variables

53y^2-2

Back to the equation:

-(53y^2-2)


We add all the numbers together, and all the variables

-(53y^2-2)=0

We get rid of parentheses

-53y^2+2=0

a = -53; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-53)·2
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{106}}{2*-53}=\frac{0-2\sqrt{106}}{-106}
=-\frac{2\sqrt{106}}{-106}
=-\frac{\sqrt{106}}{-53}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{106}}{2*-53}=\frac{0+2\sqrt{106}}{-106}
=\frac{2\sqrt{106}}{-106}
=\frac{\sqrt{106}}{-53}
$