3(2x+1)+2(4x2)=35

Solution for 3(2x+1)+2(4x2)=35 equation:

3(2x+1)+2(4x^2)=35

We move all terms to the left:

3(2x+1)+2(4x^2)-(35)=0

determiningTheFunctionDomain
24x^2+3(2x+1)-35=0

We multiply parentheses

24x^2+6x+3-35=0

We add all the numbers together, and all the variables

24x^2+6x-32=0

a = 24; b = 6; c = -32;
Δ = b2-4ac
Δ = 62-4·24·(-32)
Δ = 3108
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:

$\sqrt{\Delta}=\sqrt{3108}=\sqrt{4*777}=\sqrt{4}*\sqrt{777}=2\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{777}}{2*24}=\frac{-6-2\sqrt{777}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{777}}{2*24}=\frac{-6+2\sqrt{777}}{48}
$