2y^2-7y=5y-10

Solution for 2y^2-7y=5y-10 equation:

2y^2-7y=5y-10

We move all terms to the left:

2y^2-7y-(5y-10)=0

We get rid of parentheses

2y^2-7y-5y+10=0

We add all the numbers together, and all the variables

2y^2-12y+10=0

a = 2; b = -12; c = +10;
Δ = b2-4ac
Δ = -122-4·2·10
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*2}=\frac{4}{4}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*2}=\frac{20}{4}
=5
$