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3/4y+13=2y-2
We move all terms to the left:
3/4y+13-(2y-2)=0
Domain of the equation: 4y!=0We get rid of parentheses
y!=0/4
y!=0
y∈R
3/4y-2y+2+13=0
We multiply all the terms by the denominator
-2y*4y+2*4y+13*4y+3=0
Wy multiply elements
-8y^2+8y+52y+3=0
We add all the numbers together, and all the variables
-8y^2+60y+3=0
a = -8; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·(-8)·3
Δ = 3696
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{231}}{2*-8}=\frac{-60-4\sqrt{231}}{-16} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{231}}{2*-8}=\frac{-60+4\sqrt{231}}{-16} $
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