4x^2-3x-5=10x-2x^2

Solution for 4x^2-3x-5=10x-2x^2 equation:

4x^2-3x-5=10x-2x^2

We move all terms to the left:

4x^2-3x-5-(10x-2x^2)=0

We get rid of parentheses

4x^2+2x^2-10x-3x-5=0

We add all the numbers together, and all the variables

6x^2-13x-5=0

a = 6; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·6·(-5)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*6}=\frac{30}{12}
=2+1/2
$