2x(103-x)=6x-7

Solution for 2x(103-x)=6x-7 equation:

2x(103-x)=6x-7

We move all terms to the left:

2x(103-x)-(6x-7)=0

We add all the numbers together, and all the variables

2x(-1x+103)-(6x-7)=0

We multiply parentheses

-2x^2+206x-(6x-7)=0

We get rid of parentheses

-2x^2+206x-6x+7=0

We add all the numbers together, and all the variables

-2x^2+200x+7=0

a = -2; b = 200; c = +7;
Δ = b2-4ac
Δ = 2002-4·(-2)·7
Δ = 40056
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:

$\sqrt{\Delta}=\sqrt{40056}=\sqrt{4*10014}=\sqrt{4}*\sqrt{10014}=2\sqrt{10014}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{10014}}{2*-2}=\frac{-200-2\sqrt{10014}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{10014}}{2*-2}=\frac{-200+2\sqrt{10014}}{-4}
$