2.6(2x+3)=5x2

Solution for 2.6(2x+3)=5x2 equation:

2.6(2x+3)=5x^2

We move all terms to the left:

2.6(2x+3)-(5x^2)=0

determiningTheFunctionDomain
-5x^2+2.6(2x+3)=0

We multiply parentheses

-5x^2+5.2x+7.8=0

a = -5; b = 5.2; c = +7.8;
Δ = b2-4ac
Δ = 5.22-4·(-5)·7.8
Δ = 183.04
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{-(5.2)-\sqrt{183.04}}{2*-5}=\frac{-5.2-\sqrt{183.04}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.2)+\sqrt{183.04}}{2*-5}=\frac{-5.2+\sqrt{183.04}}{-10}
$