(3x-5)(x)=112

Solution for (3x-5)(x)=112 equation:

(3x-5)(x)=112

We move all terms to the left:

(3x-5)(x)-(112)=0

We multiply parentheses

3x^2-5x-112=0

a = 3; b = -5; c = -112;
Δ = b2-4ac
Δ = -52-4·3·(-112)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-37}{2*3}=\frac{-32}{6}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+37}{2*3}=\frac{42}{6}
=7
$