2x+10=2(x+3)x+4

Solution for 2x+10=2(x+3)x+4 equation:

2x+10=2(x+3)x+4

We move all terms to the left:

2x+10-(2(x+3)x+4)=0


We calculate terms in parentheses: -(2(x+3)x+4), so:

2(x+3)x+4

We multiply parentheses

2x^2+6x+4

Back to the equation:

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


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-2)·6
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{-(-4)-8}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-2}=\frac{12}{-4}
=-3
$