X(4x+3)=7x+5

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

X(4X+3)=7X+5

We move all terms to the left:

X(4X+3)-(7X+5)=0

We multiply parentheses

4X^2+3X-(7X+5)=0

We get rid of parentheses

4X^2+3X-7X-5=0

We add all the numbers together, and all the variables

4X^2-4X-5=0

a = 4; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·4·(-5)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*4}=\frac{4-4\sqrt{6}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*4}=\frac{4+4\sqrt{6}}{8}
$