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=5Y+3/4Y-7
We move all terms to the left:
-(5Y+3/4Y-7)=0
Domain of the equation: 4Y-7)!=0We get rid of parentheses
Y∈R
-5Y-3/4Y+7=0
We multiply all the terms by the denominator
-5Y*4Y+7*4Y-3=0
Wy multiply elements
-20Y^2+28Y-3=0
a = -20; b = 28; c = -3;
Δ = b2-4ac
Δ = 282-4·(-20)·(-3)
Δ = 544
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{34}}{2*-20}=\frac{-28-4\sqrt{34}}{-40} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{34}}{2*-20}=\frac{-28+4\sqrt{34}}{-40} $
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