3x2-17=8-10X

Solution for 3x2-17=8-10X equation:

3x^2-17=8-10x

We move all terms to the left:

3x^2-17-(8-10x)=0

We add all the numbers together, and all the variables

3x^2-(-10x+8)-17=0

We get rid of parentheses

3x^2+10x-8-17=0

We add all the numbers together, and all the variables

3x^2+10x-25=0

a = 3; b = 10; c = -25;
Δ = b2-4ac
Δ = 102-4·3·(-25)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20}{2*3}=\frac{10}{6}
=1+2/3
$