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

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
$