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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(5x(x+3)+2), so:

5x(x+3)+2

We multiply parentheses

5x^2+15x+2

Back to the equation:

-(5x^2+15x+2)


We get rid of parentheses

-5x^2-7x-15x-2+5=0

We add all the numbers together, and all the variables

-5x^2-22x+3=0

a = -5; b = -22; c = +3;
Δ = b2-4ac
Δ = -222-4·(-5)·3
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{34}}{2*-5}=\frac{22-4\sqrt{34}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{34}}{2*-5}=\frac{22+4\sqrt{34}}{-10}
$