2x(2+3x)=26x+868

Solution for 2x(2+3x)=26x+868 equation:

2x(2+3x)=26x+868

We move all terms to the left:

2x(2+3x)-(26x+868)=0

We add all the numbers together, and all the variables

2x(3x+2)-(26x+868)=0

We multiply parentheses

6x^2+4x-(26x+868)=0

We get rid of parentheses

6x^2+4x-26x-868=0

We add all the numbers together, and all the variables

6x^2-22x-868=0

a = 6; b = -22; c = -868;
Δ = b2-4ac
Δ = -222-4·6·(-868)
Δ = 21316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21316}=146$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-146}{2*6}=\frac{-124}{12}
=-10+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+146}{2*6}=\frac{168}{12}
=14
$