2(1.2x+0.3)(x-0.5)+(0.5x^2+2.5x-1.3)=0

Solution for 2(1.2x+0.3)(x-0.5)+(0.5x^2+2.5x-1.3)=0 equation:

2(1.2x+0.3)(x-0.5)+(0.5x^2+2.5x-1.3)=0

We get rid of parentheses

0.5x^2+2(1.2x+0.3)(x-0.5)+2.5x-1.3=0

We multiply parentheses ..

0.5x^2+2(+x^2-0.5x+0.3x-0.15)+2.5x-1.3=0

We multiply parentheses

0.5x^2+2x^2+0x+0x+2.5x-0.3-1.3=0

We add all the numbers together, and all the variables

2.5x^2+4.5x-1.6=0

a = 2.5; b = 4.5; c = -1.6;
Δ = b2-4ac
Δ = 4.52-4·2.5·(-1.6)
Δ = 36.25
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{-(4.5)-\sqrt{36.25}}{2*2.5}=\frac{-4.5-\sqrt{36.25}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{36.25}}{2*2.5}=\frac{-4.5+\sqrt{36.25}}{5}
$