7(1-2x)-3=4-x2

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Solution for 7(1-2x)-3=4-x2 equation:



7(1-2x)-3=4-x2
We move all terms to the left:
7(1-2x)-3-(4-x2)=0
We add all the numbers together, and all the variables
-(-1x^2+4)+7(-2x+1)-3=0
We multiply parentheses
-(-1x^2+4)-14x+7-3=0
We get rid of parentheses
1x^2-14x-4+7-3=0
We add all the numbers together, and all the variables
x^2-14x=0
a = 1; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·1·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*1}=\frac{0}{2} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*1}=\frac{28}{2} =14 $

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