(2x-1)(3x+4)=7

Solution for (2x-1)(3x+4)=7 equation:

(2x-1)(3x+4)=7

We move all terms to the left:

(2x-1)(3x+4)-(7)=0

We multiply parentheses ..

(+6x^2+8x-3x-4)-7=0

We get rid of parentheses

6x^2+8x-3x-4-7=0

We add all the numbers together, and all the variables

6x^2+5x-11=0

a = 6; b = 5; c = -11;
Δ = b2-4ac
Δ = 52-4·6·(-11)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*6}=\frac{-22}{12}
=-1+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*6}=\frac{12}{12}
=1
$