2(4-5x)=3x^2

Solution for 2(4-5x)=3x^2 equation:

2(4-5x)=3x^2

We move all terms to the left:

2(4-5x)-(3x^2)=0

determiningTheFunctionDomain
-3x^2+2(4-5x)=0

We add all the numbers together, and all the variables

-3x^2+2(-5x+4)=0

We multiply parentheses

-3x^2-10x+8=0

a = -3; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·(-3)·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*-3}=\frac{-4}{-6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*-3}=\frac{24}{-6}
=-4
$