4(x+5)=6(2x2)

Solution for 4(x+5)=6(2x2) equation:

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

We move all terms to the left:

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

determiningTheFunctionDomain
4(x+5)-62x^2=0

We add all the numbers together, and all the variables

-62x^2+4(x+5)=0

We multiply parentheses

-62x^2+4x+20=0

a = -62; b = 4; c = +20;
Δ = b2-4ac
Δ = 42-4·(-62)·20
Δ = 4976
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:

$\sqrt{\Delta}=\sqrt{4976}=\sqrt{16*311}=\sqrt{16}*\sqrt{311}=4\sqrt{311}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{311}}{2*-62}=\frac{-4-4\sqrt{311}}{-124}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{311}}{2*-62}=\frac{-4+4\sqrt{311}}{-124}
$