(4x-1)(2x+3)=49

Solution for (4x-1)(2x+3)=49 equation:

(4x-1)(2x+3)=49

We move all terms to the left:

(4x-1)(2x+3)-(49)=0

We multiply parentheses ..

(+8x^2+12x-2x-3)-49=0

We get rid of parentheses

8x^2+12x-2x-3-49=0

We add all the numbers together, and all the variables

8x^2+10x-52=0

a = 8; b = 10; c = -52;
Δ = b2-4ac
Δ = 102-4·8·(-52)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-42}{2*8}=\frac{-52}{16}
=-3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+42}{2*8}=\frac{32}{16}
=2
$