(12x)(2)=78-2x

Solution for (12x)(2)=78-2x equation:

(12x)(2)=78-2x

We move all terms to the left:

(12x)(2)-(78-2x)=0

We add all the numbers together, and all the variables

12x2-(-2x+78)=0

We add all the numbers together, and all the variables

12x^2-(-2x+78)=0

We get rid of parentheses

12x^2+2x-78=0

a = 12; b = 2; c = -78;
Δ = b2-4ac
Δ = 22-4·12·(-78)
Δ = 3748
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:

$\sqrt{\Delta}=\sqrt{3748}=\sqrt{4*937}=\sqrt{4}*\sqrt{937}=2\sqrt{937}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{937}}{2*12}=\frac{-2-2\sqrt{937}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{937}}{2*12}=\frac{-2+2\sqrt{937}}{24}
$