(C-4)(x-18)=x(x-14)

Solution for (C-4)(x-18)=x(x-14) equation:

(-4)(C-18)=C(C-14)

We move all terms to the left:

(-4)(C-18)-(C(C-14))=0

We multiply parentheses ..

(-4C+72)-(C(C-14))=0


We calculate terms in parentheses: -(C(C-14)), so:

C(C-14)

We multiply parentheses

C^2-14C

Back to the equation:

-(C^2-14C)


We get rid of parentheses

-C^2-4C+14C+72=0

We add all the numbers together, and all the variables

-1C^2+10C+72=0

a = -1; b = 10; c = +72;
Δ = b2-4ac
Δ = 102-4·(-1)·72
Δ = 388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{97}}{2*-1}=\frac{-10-2\sqrt{97}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{97}}{2*-1}=\frac{-10+2\sqrt{97}}{-2}
$