(4x+3)(x-2)=42

Solution for (4x+3)(x-2)=42 equation:

(4x+3)(x-2)=42

We move all terms to the left:

(4x+3)(x-2)-(42)=0

We multiply parentheses ..

(+4x^2-8x+3x-6)-42=0

We get rid of parentheses

4x^2-8x+3x-6-42=0

We add all the numbers together, and all the variables

4x^2-5x-48=0

a = 4; b = -5; c = -48;
Δ = b2-4ac
Δ = -52-4·4·(-48)
Δ = 793
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{-(-5)-\sqrt{793}}{2*4}=\frac{5-\sqrt{793}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{793}}{2*4}=\frac{5+\sqrt{793}}{8}
$