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=4Y-3/5Y+2
We move all terms to the left:
-(4Y-3/5Y+2)=0
Domain of the equation: 5Y+2)!=0We get rid of parentheses
Y∈R
-4Y+3/5Y-2=0
We multiply all the terms by the denominator
-4Y*5Y-2*5Y+3=0
Wy multiply elements
-20Y^2-10Y+3=0
a = -20; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·(-20)·3
Δ = 340
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*-20}=\frac{10-2\sqrt{85}}{-40} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*-20}=\frac{10+2\sqrt{85}}{-40} $
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