X(4x-3)=154

Solution for X(4x-3)=154 equation:

X(4X-3)=154

We move all terms to the left:

X(4X-3)-(154)=0

We multiply parentheses

4X^2-3X-154=0

a = 4; b = -3; c = -154;
Δ = b2-4ac
Δ = -32-4·4·(-154)
Δ = 2473
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{2473}}{2*4}=\frac{3-\sqrt{2473}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{2473}}{2*4}=\frac{3+\sqrt{2473}}{8}
$