25y+15-16y=7y+11/2y-9

Solution for 25y+15-16y=7y+11/2y-9 equation:

25y+15-16y=7y+11/2y-9

We move all terms to the left:

25y+15-16y-(7y+11/2y-9)=0


Domain of the equation: 2y-9)!=0

y∈R


We add all the numbers together, and all the variables

9y-(7y+11/2y-9)+15=0

We get rid of parentheses

9y-7y-11/2y+9+15=0

We multiply all the terms by the denominator


9y*2y-7y*2y+9*2y+15*2y-11=0

Wy multiply elements

18y^2-14y^2+18y+30y-11=0

We add all the numbers together, and all the variables

4y^2+48y-11=0

a = 4; b = 48; c = -11;
Δ = b2-4ac
Δ = 482-4·4·(-11)
Δ = 2480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2480}=\sqrt{16*155}=\sqrt{16}*\sqrt{155}=4\sqrt{155}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{155}}{2*4}=\frac{-48-4\sqrt{155}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{155}}{2*4}=\frac{-48+4\sqrt{155}}{8}
$