0.5(6x^2+3x-2)=(2x^2-x+5)

Solution for 0.5(6x^2+3x-2)=(2x^2-x+5) equation:

0.5(6x^2+3x-2)=(2x^2-x+5)

We move all terms to the left:

0.5(6x^2+3x-2)-((2x^2-x+5))=0

We multiply parentheses

3x^2+1.5x-((2x^2-x+5))-1=0


We calculate terms in parentheses: -((2x^2-x+5)), so:

(2x^2-x+5)

We get rid of parentheses

2x^2-x+5

We add all the numbers together, and all the variables

2x^2-1x+5

Back to the equation:

-(2x^2-1x+5)


We get rid of parentheses

3x^2-2x^2+1.5x+1x-5-1=0

We add all the numbers together, and all the variables

x^2+2.5x-6=0

a = 1; b = 2.5; c = -6;
Δ = b2-4ac
Δ = 2.52-4·1·(-6)
Δ = 30.25
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{-(2.5)-\sqrt{30.25}}{2*1}=\frac{-2.5-\sqrt{30.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{30.25}}{2*1}=\frac{-2.5+\sqrt{30.25}}{2}
$