(60+3x)*(80-2x)=5346

Solution for (60+3x)*(80-2x)=5346 equation:

(60+3x)(80-2x)=5346

We move all terms to the left:

(60+3x)(80-2x)-(5346)=0

We add all the numbers together, and all the variables

(3x+60)(-2x+80)-5346=0

We multiply parentheses ..

(-6x^2+240x-120x+4800)-5346=0

We get rid of parentheses

-6x^2+240x-120x+4800-5346=0

We add all the numbers together, and all the variables

-6x^2+120x-546=0

a = -6; b = 120; c = -546;
Δ = b2-4ac
Δ = 1202-4·(-6)·(-546)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-36}{2*-6}=\frac{-156}{-12}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+36}{2*-6}=\frac{-84}{-12}
=+7
$