10x+30=18x2

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Solution for 10x+30=18x2 equation:



10x+30=18x^2
We move all terms to the left:
10x+30-(18x^2)=0
determiningTheFunctionDomain -18x^2+10x+30=0
a = -18; b = 10; c = +30;
Δ = b2-4ac
Δ = 102-4·(-18)·30
Δ = 2260
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:
$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{565}}{2*-18}=\frac{-10-2\sqrt{565}}{-36} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{565}}{2*-18}=\frac{-10+2\sqrt{565}}{-36} $

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