(4x-7)(3x+8)=5

Solution for (4x-7)(3x+8)=5 equation:

(4x-7)(3x+8)=5

We move all terms to the left:

(4x-7)(3x+8)-(5)=0

We multiply parentheses ..

(+12x^2+32x-21x-56)-5=0

We get rid of parentheses

12x^2+32x-21x-56-5=0

We add all the numbers together, and all the variables

12x^2+11x-61=0

a = 12; b = 11; c = -61;
Δ = b2-4ac
Δ = 112-4·12·(-61)
Δ = 3049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{3049}}{2*12}=\frac{-11-\sqrt{3049}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{3049}}{2*12}=\frac{-11+\sqrt{3049}}{24}
$