((7*4y)*3.5y)+((3*4y)*6.5y)=40

Solution for ((7*4y)*3.5y)+((3*4y)*6.5y)=40 equation:

((7*4y)*3.5y)+((3*4y)*6.5y)=40

We move all terms to the left:

((7*4y)*3.5y)+((3*4y)*6.5y)-(40)=0

We add all the numbers together, and all the variables

((+7*4y)*3.5y)+((+3*4y)*6.5y)-40=0


We calculate terms in parentheses: +((+7*4y)*3.5y), so:

(+7*4y)*3.5y

We multiply parentheses

84y^2

Back to the equation:

+(84y^2)



We calculate terms in parentheses: +((+3*4y)*6.5y), so:

(+3*4y)*6.5y

We multiply parentheses

72y^2

Back to the equation:

+(72y^2)


We add all the numbers together, and all the variables

156y^2-40=0

a = 156; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·156·(-40)
Δ = 24960
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:

$\sqrt{\Delta}=\sqrt{24960}=\sqrt{64*390}=\sqrt{64}*\sqrt{390}=8\sqrt{390}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{390}}{2*156}=\frac{0-8\sqrt{390}}{312}
=-\frac{8\sqrt{390}}{312}
=-\frac{\sqrt{390}}{39}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{390}}{2*156}=\frac{0+8\sqrt{390}}{312}
=\frac{8\sqrt{390}}{312}
=\frac{\sqrt{390}}{39}
$