5x-2+3x=3(x+4)5x-10

Solution for 5x-2+3x=3(x+4)5x-10 equation:

5x-2+3x=3(x+4)5x-10

We move all terms to the left:

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

We add all the numbers together, and all the variables

8x-(3(x+4)5x-10)-2=0


We calculate terms in parentheses: -(3(x+4)5x-10), so:

3(x+4)5x-10

We multiply parentheses

15x^2+60x-10

Back to the equation:

-(15x^2+60x-10)


We get rid of parentheses

-15x^2+8x-60x+10-2=0

We add all the numbers together, and all the variables

-15x^2-52x+8=0

a = -15; b = -52; c = +8;
Δ = b2-4ac
Δ = -522-4·(-15)·8
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{199}}{2*-15}=\frac{52-4\sqrt{199}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{199}}{2*-15}=\frac{52+4\sqrt{199}}{-30}
$