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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-7x-10=0

a = 3; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·3·(-10)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*3}=\frac{20}{6}
=3+1/3
$