X2-4x+18=10x-30

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Solution for X2-4x+18=10x-30 equation:



X2-4X+18=10X-30
We move all terms to the left:
X2-4X+18-(10X-30)=0
We add all the numbers together, and all the variables
X^2-4X-(10X-30)+18=0
We get rid of parentheses
X^2-4X-10X+30+18=0
We add all the numbers together, and all the variables
X^2-14X+48=0
a = 1; b = -14; c = +48;
Δ = b2-4ac
Δ = -142-4·1·48
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2}{2*1}=\frac{12}{2} =6 $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*1}=\frac{16}{2} =8 $

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