X.7(8+7x)=133

Solution for X.7(8+7x)=133 equation:

X.7(8+7X)=133

We move all terms to the left:

X.7(8+7X)-(133)=0

We add all the numbers together, and all the variables

X.7(7X+8)-133=0

We multiply parentheses

7X^2+8X-133=0

a = 7; b = 8; c = -133;
Δ = b2-4ac
Δ = 82-4·7·(-133)
Δ = 3788
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:

$\sqrt{\Delta}=\sqrt{3788}=\sqrt{4*947}=\sqrt{4}*\sqrt{947}=2\sqrt{947}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{947}}{2*7}=\frac{-8-2\sqrt{947}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{947}}{2*7}=\frac{-8+2\sqrt{947}}{14}
$