3x=10-x2

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Solution for 3x=10-x2 equation:



3x=10-x2
We move all terms to the left:
3x-(10-x2)=0
We add all the numbers together, and all the variables
-(-1x^2+10)+3x=0
We get rid of parentheses
1x^2+3x-10=0
We add all the numbers together, and all the variables
x^2+3x-10=0
a = 1; b = 3; c = -10;
Δ = b2-4ac
Δ = 32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7}{2*1}=\frac{-10}{2} =-5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*1}=\frac{4}{2} =2 $

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