10-4y(7-10y)=18

Solution for 10-4y(7-10y)=18 equation:

10-4y(7-10y)=18

We move all terms to the left:

10-4y(7-10y)-(18)=0

We add all the numbers together, and all the variables

-4y(-10y+7)+10-18=0

We add all the numbers together, and all the variables

-4y(-10y+7)-8=0

We multiply parentheses

40y^2-28y-8=0

a = 40; b = -28; c = -8;
Δ = b2-4ac
Δ = -282-4·40·(-8)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{129}}{2*40}=\frac{28-4\sqrt{129}}{80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{129}}{2*40}=\frac{28+4\sqrt{129}}{80}
$