Y=(2x)2-3x-7

Solution for Y=(2x)2-3x-7 equation:

=(2Y)2-3Y-7

We move all terms to the left:

-((2Y)2-3Y-7)=0

We add all the numbers together, and all the variables

-(+2Y^2-3Y-7)=0

We get rid of parentheses

-2Y^2+3Y+7=0

a = -2; b = 3; c = +7;
Δ = b2-4ac
Δ = 32-4·(-2)·7
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{65}}{2*-2}=\frac{-3-\sqrt{65}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{65}}{2*-2}=\frac{-3+\sqrt{65}}{-4}
$