5x+30=10x2

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Solution for 5x+30=10x2 equation:



5x+30=10x^2
We move all terms to the left:
5x+30-(10x^2)=0
determiningTheFunctionDomain -10x^2+5x+30=0
a = -10; b = 5; c = +30;
Δ = b2-4ac
Δ = 52-4·(-10)·30
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*-10}=\frac{-40}{-20} =+2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*-10}=\frac{30}{-20} =-1+1/2 $

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