4x2-10x-2=2(2x+3)

Solution for 4x2-10x-2=2(2x+3) equation:

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

We move all terms to the left:

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


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

2(2x+3)

We multiply parentheses

4x+6

Back to the equation:

-(4x+6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-14x-8=0

a = 4; b = -14; c = -8;
Δ = b2-4ac
Δ = -142-4·4·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-18}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+18}{2*4}=\frac{32}{8}
=4
$