2/3x=10x-30

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Solution for 2/3x=10x-30 equation:



2/3x=10x-30
We move all terms to the left:
2/3x-(10x-30)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We get rid of parentheses
2/3x-10x+30=0
We multiply all the terms by the denominator
-10x*3x+30*3x+2=0
Wy multiply elements
-30x^2+90x+2=0
a = -30; b = 90; c = +2;
Δ = b2-4ac
Δ = 902-4·(-30)·2
Δ = 8340
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:
$\sqrt{\Delta}=\sqrt{8340}=\sqrt{4*2085}=\sqrt{4}*\sqrt{2085}=2\sqrt{2085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2085}}{2*-30}=\frac{-90-2\sqrt{2085}}{-60} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2085}}{2*-30}=\frac{-90+2\sqrt{2085}}{-60} $

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