6(3x+6)=4(5x2)

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Solution for 6(3x+6)=4(5x2) equation:



6(3x+6)=4(5x^2)
We move all terms to the left:
6(3x+6)-(4(5x^2))=0
determiningTheFunctionDomain 6(3x+6)-45x^2=0
We add all the numbers together, and all the variables
-45x^2+6(3x+6)=0
We multiply parentheses
-45x^2+18x+36=0
a = -45; b = 18; c = +36;
Δ = b2-4ac
Δ = 182-4·(-45)·36
Δ = 6804
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:
$\sqrt{\Delta}=\sqrt{6804}=\sqrt{324*21}=\sqrt{324}*\sqrt{21}=18\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{21}}{2*-45}=\frac{-18-18\sqrt{21}}{-90} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{21}}{2*-45}=\frac{-18+18\sqrt{21}}{-90} $

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