(x+6)(4x+3)=2x+3)^2

Solution for (x+6)(4x+3)=2x+3)^2 equation:

(x+6)(4x+3)=2x+3)^2

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+4x^2+3x+24x+18)-2x-3)^2=0

We add all the numbers together, and all the variables

(+4x^2+3x+24x+18)-2x=0

We get rid of parentheses

4x^2+3x+24x-2x+18=0

We add all the numbers together, and all the variables

4x^2+25x+18=0

a = 4; b = 25; c = +18;
Δ = b2-4ac
Δ = 252-4·4·18
Δ = 337
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{-(25)-\sqrt{337}}{2*4}=\frac{-25-\sqrt{337}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{337}}{2*4}=\frac{-25+\sqrt{337}}{8}
$