(6y^2-5)-(4y^2-5y+2)=0

Solution for (6y^2-5)-(4y^2-5y+2)=0 equation:

(6y^2-5)-(4y^2-5y+2)=0

We get rid of parentheses

6y^2-4y^2+5y-5-2=0

We add all the numbers together, and all the variables

2y^2+5y-7=0

a = 2; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·2·(-7)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*2}=\frac{-14}{4}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*2}=\frac{4}{4}
=1
$