4x+3.5=2(2x+2)x

Solution for 4x+3.5=2(2x+2)x equation:

4x+3.5=2(2x+2)x

We move all terms to the left:

4x+3.5-(2(2x+2)x)=0


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

2(2x+2)x

We multiply parentheses

4x^2+4x

Back to the equation:

-(4x^2+4x)


We get rid of parentheses

-4x^2+4x-4x+3.5=0

We add all the numbers together, and all the variables

-4x^2+3.5=0

a = -4; b = 0; c = +3.5;
Δ = b2-4ac
Δ = 02-4·(-4)·3.5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*-4}=\frac{0-2\sqrt{14}}{-8}
=-\frac{2\sqrt{14}}{-8}
=-\frac{\sqrt{14}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-4}=\frac{0+2\sqrt{14}}{-8}
=\frac{2\sqrt{14}}{-8}
=\frac{\sqrt{14}}{-4}
$