5+2x(x-4)=4x+7

Solution for 5+2x(x-4)=4x+7 equation:

5+2x(x-4)=4x+7

We move all terms to the left:

5+2x(x-4)-(4x+7)=0

We multiply parentheses

2x^2-8x-(4x+7)+5=0

We get rid of parentheses

2x^2-8x-4x-7+5=0

We add all the numbers together, and all the variables

2x^2-12x-2=0

a = 2; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·2·(-2)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*2}=\frac{12-4\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*2}=\frac{12+4\sqrt{10}}{4}
$