180x-14x^2=298+12x

Solution for 180x-14x^2=298+12x equation:

180x-14x^2=298+12x

We move all terms to the left:

180x-14x^2-(298+12x)=0

We add all the numbers together, and all the variables

-14x^2+180x-(12x+298)=0

We get rid of parentheses

-14x^2+180x-12x-298=0

We add all the numbers together, and all the variables

-14x^2+168x-298=0

a = -14; b = 168; c = -298;
Δ = b2-4ac
Δ = 1682-4·(-14)·(-298)
Δ = 11536
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:

$\sqrt{\Delta}=\sqrt{11536}=\sqrt{16*721}=\sqrt{16}*\sqrt{721}=4\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-4\sqrt{721}}{2*-14}=\frac{-168-4\sqrt{721}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+4\sqrt{721}}{2*-14}=\frac{-168+4\sqrt{721}}{-28}
$