4-2(x-7)x=3

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

4-2(x-7)x=3

We move all terms to the left:

4-2(x-7)x-(3)=0

We add all the numbers together, and all the variables

-2(x-7)x+1=0

We multiply parentheses

-2x^2+14x+1=0

a = -2; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-2)·1
Δ = 204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{51}}{2*-2}=\frac{-14-2\sqrt{51}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{51}}{2*-2}=\frac{-14+2\sqrt{51}}{-4}
$