2(4x+3)=10x2

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

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

We move all terms to the left:

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

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

We multiply parentheses

-10x^2+8x+6=0

a = -10; b = 8; c = +6;
Δ = b2-4ac
Δ = 82-4·(-10)·6
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{19}}{2*-10}=\frac{-8-4\sqrt{19}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{19}}{2*-10}=\frac{-8+4\sqrt{19}}{-20}
$