6x^2-10x=+3x-5

Solution for 6x^2-10x=+3x-5 equation:

6x^2-10x=+3x-5

We move all terms to the left:

6x^2-10x-(+3x-5)=0

We add all the numbers together, and all the variables

6x^2-10x-(3x-5)=0

We get rid of parentheses

6x^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 = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*6}=\frac{20}{12}
=1+2/3
$