3x-0.5+5x-2=2x+3x2+10x-5

Solution for 3x-0.5+5x-2=2x+3x2+10x-5 equation:

3x-0.5+5x-2=2x+3x^2+10x-5

We move all terms to the left:

3x-0.5+5x-2-(2x+3x^2+10x-5)=0

We add all the numbers together, and all the variables

-(2x+3x^2+10x-5)+8x-2.5=0

We get rid of parentheses

-3x^2-2x-10x+8x+5-2.5=0

We add all the numbers together, and all the variables

-3x^2-4x+2.5=0

a = -3; b = -4; c = +2.5;
Δ = b2-4ac
Δ = -42-4·(-3)·2.5
Δ = 46
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)-\sqrt{46}}{2*-3}=\frac{4-\sqrt{46}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{46}}{2*-3}=\frac{4+\sqrt{46}}{-6}
$