3x+8/5x-9=0

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Solution for 3x+8/5x-9=0 equation: 



3x+8/5x-9=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We multiply all the terms by the denominator


3x*5x-9*5x+8=0

Wy multiply elements

15x^2-45x+8=0

a = 15; b = -45; c = +8;
Δ = b2-4ac
Δ = -452-4·15·8
Δ = 1545
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1545}}{2*15}=\frac{45-\sqrt{1545}}{30}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1545}}{2*15}=\frac{45+\sqrt{1545}}{30}
$

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