x2+4x+10=5x+30

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Solution for x2+4x+10=5x+30 equation:



x2+4x+10=5x+30
We move all terms to the left:
x2+4x+10-(5x+30)=0
We add all the numbers together, and all the variables
x^2+4x-(5x+30)+10=0
We get rid of parentheses
x^2+4x-5x-30+10=0
We add all the numbers together, and all the variables
x^2-1x-20=0
a = 1; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·1·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*1}=\frac{-8}{2} =-4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*1}=\frac{10}{2} =5 $

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