5x^2-7x-2=3x

Solution for 5x^2-7x-2=3x equation:

5x^2-7x-2=3x

We move all terms to the left:

5x^2-7x-2-(3x)=0

We add all the numbers together, and all the variables

5x^2-10x-2=0

a = 5; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·5·(-2)
Δ = 140
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{35}}{2*5}=\frac{10-2\sqrt{35}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{35}}{2*5}=\frac{10+2\sqrt{35}}{10}
$