3x^2-8-10x=3(2x+3)

Solution for 3x^2-8-10x=3(2x+3) equation:

3x^2-8-10x=3(2x+3)

We move all terms to the left:

3x^2-8-10x-(3(2x+3))=0


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

3(2x+3)

We multiply parentheses

6x+9

Back to the equation:

-(6x+9)


We get rid of parentheses

3x^2-10x-6x-9-8=0

We add all the numbers together, and all the variables

3x^2-16x-17=0

a = 3; b = -16; c = -17;
Δ = b2-4ac
Δ = -162-4·3·(-17)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{115}}{2*3}=\frac{16-2\sqrt{115}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{115}}{2*3}=\frac{16+2\sqrt{115}}{6}
$