(3x+4)(2x-1)=112

Solution for (3x+4)(2x-1)=112 equation:

(3x+4)(2x-1)=112

We move all terms to the left:

(3x+4)(2x-1)-(112)=0

We multiply parentheses ..

(+6x^2-3x+8x-4)-112=0

We get rid of parentheses

6x^2-3x+8x-4-112=0

We add all the numbers together, and all the variables

6x^2+5x-116=0

a = 6; b = 5; c = -116;
Δ = b2-4ac
Δ = 52-4·6·(-116)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-53}{2*6}=\frac{-58}{12}
=-4+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+53}{2*6}=\frac{48}{12}
=4
$