8(x-3)+7=(4-17)x2x

Solution for 8(x-3)+7=(4-17)x2x equation:

8(x-3)+7=(4-17)x2x

We move all terms to the left:

8(x-3)+7-((4-17)x2x)=0

We add all the numbers together, and all the variables

8(x-3)-((-13)x2x)+7=0

We multiply parentheses

8x-((-13)x2x)-24+7=0


We calculate terms in parentheses: -((-13)x2x), so:

(-13)x2x

We multiply parentheses

-13x^2

Back to the equation:

-(-13x^2)


We add all the numbers together, and all the variables

-(-13x^2)+8x-17=0

We get rid of parentheses

13x^2+8x-17=0

a = 13; b = 8; c = -17;
Δ = b2-4ac
Δ = 82-4·13·(-17)
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{237}}{2*13}=\frac{-8-2\sqrt{237}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{237}}{2*13}=\frac{-8+2\sqrt{237}}{26}
$