7-(4y-3)y=6

Solution for 7-(4y-3)y=6 equation:

7-(4y-3)y=6

We move all terms to the left:

7-(4y-3)y-(6)=0

We add all the numbers together, and all the variables

-(4y-3)y+1=0

We multiply parentheses

-4y^2+3y+1=0

a = -4; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-4)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-4}=\frac{-8}{-8}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-4}=\frac{2}{-8}
=-1/4
$