2y+23y=7y^2-1

Solution for 2y+23y=7y^2-1 equation:

2y+23y=7y^2-1

We move all terms to the left:

2y+23y-(7y^2-1)=0

We add all the numbers together, and all the variables

25y-(7y^2-1)=0

We get rid of parentheses

-7y^2+25y+1=0

a = -7; b = 25; c = +1;
Δ = b2-4ac
Δ = 252-4·(-7)·1
Δ = 653
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{-(25)-\sqrt{653}}{2*-7}=\frac{-25-\sqrt{653}}{-14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{653}}{2*-7}=\frac{-25+\sqrt{653}}{-14}
$