5x2-17.5x-10=x2+6x+30

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Solution for 5x2-17.5x-10=x2+6x+30 equation:



5x^2-17.5x-10=x2+6x+30
We move all terms to the left:
5x^2-17.5x-10-(x2+6x+30)=0
We add all the numbers together, and all the variables
5x^2-(+x^2+6x+30)-17.5x-10=0
We get rid of parentheses
5x^2-x^2-6x-17.5x-30-10=0
We add all the numbers together, and all the variables
4x^2-23.5x-40=0
a = 4; b = -23.5; c = -40;
Δ = b2-4ac
Δ = -23.52-4·4·(-40)
Δ = 1192.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23.5)-\sqrt{1192.25}}{2*4}=\frac{23.5-\sqrt{1192.25}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23.5)+\sqrt{1192.25}}{2*4}=\frac{23.5+\sqrt{1192.25}}{8} $

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