3x+90/2x+90=0

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Solution for 3x+90/2x+90=0 equation: 



3x+90/2x+90=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We multiply all the terms by the denominator


3x*2x+90*2x+90=0

Wy multiply elements

6x^2+180x+90=0

a = 6; b = 180; c = +90;
Δ = b2-4ac
Δ = 1802-4·6·90
Δ = 30240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{30240}=\sqrt{144*210}=\sqrt{144}*\sqrt{210}=12\sqrt{210}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{210}}{2*6}=\frac{-180-12\sqrt{210}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{210}}{2*6}=\frac{-180+12\sqrt{210}}{12}
$

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