(1.5x-2.4)2=(5.2x2-6.4)

Solution for (1.5x-2.4)2=(5.2x2-6.4) equation:

(1.5x-2.4)2=(5.2x^2-6.4)

We move all terms to the left:

(1.5x-2.4)2-((5.2x^2-6.4))=0

We multiply parentheses

2x-((5.2x^2-6.4))-4.8=0


We calculate terms in parentheses: -((5.2x^2-6.4)), so:

(5.2x^2-6.4)

We get rid of parentheses

5.2x^2-6.4

Back to the equation:

-(5.2x^2-6.4)


We get rid of parentheses

-5.2x^2+2x+6.4-4.8=0

We add all the numbers together, and all the variables

-5.2x^2+2x+1.6=0

a = -5.2; b = 2; c = +1.6;
Δ = b2-4ac
Δ = 22-4·(-5.2)·1.6
Δ = 37.28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-\sqrt{37.28}}{2*-5.2}=\frac{-2-\sqrt{37.28}}{-10.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{37.28}}{2*-5.2}=\frac{-2+\sqrt{37.28}}{-10.4}
$