(Y-4)=2x(x-7)

Solution for (Y-4)=2x(x-7) equation:

(-4)=2Y(Y-7)

We move all terms to the left:

(-4)-(2Y(Y-7))=0

We add all the numbers together, and all the variables

-(2Y(Y-7))-4=0


We calculate terms in parentheses: -(2Y(Y-7)), so:

2Y(Y-7)

We multiply parentheses

2Y^2-14Y

Back to the equation:

-(2Y^2-14Y)


We get rid of parentheses

-2Y^2+14Y-4=0

a = -2; b = 14; c = -4;
Δ = b2-4ac
Δ = 142-4·(-2)·(-4)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{41}}{2*-2}=\frac{-14-2\sqrt{41}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{41}}{2*-2}=\frac{-14+2\sqrt{41}}{-4}
$