7x+1=2x(2x+11)

Solution for 7x+1=2x(2x+11) equation:

7x+1=2x(2x+11)

We move all terms to the left:

7x+1-(2x(2x+11))=0


We calculate terms in parentheses: -(2x(2x+11)), so:

2x(2x+11)

We multiply parentheses

4x^2+22x

Back to the equation:

-(4x^2+22x)


We get rid of parentheses

-4x^2+7x-22x+1=0

We add all the numbers together, and all the variables

-4x^2-15x+1=0

a = -4; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-4)·1
Δ = 241
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{-(-15)-\sqrt{241}}{2*-4}=\frac{15-\sqrt{241}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{241}}{2*-4}=\frac{15+\sqrt{241}}{-8}
$