X(2x-25x)+154=77

Solution for X(2x-25x)+154=77 equation:

X(2X-25X)+154=77

We move all terms to the left:

X(2X-25X)+154-(77)=0

We add all the numbers together, and all the variables

X(-23X)+154-77=0

We add all the numbers together, and all the variables

X(-23X)+77=0

We multiply parentheses

-23X^2+77=0

a = -23; b = 0; c = +77;
Δ = b2-4ac
Δ = 02-4·(-23)·77
Δ = 7084
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:

$\sqrt{\Delta}=\sqrt{7084}=\sqrt{4*1771}=\sqrt{4}*\sqrt{1771}=2\sqrt{1771}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1771}}{2*-23}=\frac{0-2\sqrt{1771}}{-46}
=-\frac{2\sqrt{1771}}{-46}
=-\frac{\sqrt{1771}}{-23}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1771}}{2*-23}=\frac{0+2\sqrt{1771}}{-46}
=\frac{2\sqrt{1771}}{-46}
=\frac{\sqrt{1771}}{-23}
$