x^2+4x-6=2(2x+5)

Solution for x^2+4x-6=2(2x+5) equation:

x^2+4x-6=2(2x+5)

We move all terms to the left:

x^2+4x-6-(2(2x+5))=0


We calculate terms in parentheses: -(2(2x+5)), so:

2(2x+5)

We multiply parentheses

4x+10

Back to the equation:

-(4x+10)


We get rid of parentheses

x^2+4x-4x-10-6=0

We add all the numbers together, and all the variables

x^2-16=0

a = 1; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1·(-16)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*1}=\frac{8}{2}
=4
$