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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+8x^2+12x-2x-3)-7x=0

We get rid of parentheses

8x^2+12x-2x-7x-3=0

We add all the numbers together, and all the variables

8x^2+3x-3=0

a = 8; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·8·(-3)
Δ = 105
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{-(3)-\sqrt{105}}{2*8}=\frac{-3-\sqrt{105}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*8}=\frac{-3+\sqrt{105}}{16}
$