X(3x-5)=275

Solution for X(3x-5)=275 equation:

X(3X-5)=275

We move all terms to the left:

X(3X-5)-(275)=0

We multiply parentheses

3X^2-5X-275=0

a = 3; b = -5; c = -275;
Δ = b2-4ac
Δ = -52-4·3·(-275)
Δ = 3325
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:

$\sqrt{\Delta}=\sqrt{3325}=\sqrt{25*133}=\sqrt{25}*\sqrt{133}=5\sqrt{133}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{133}}{2*3}=\frac{5-5\sqrt{133}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{133}}{2*3}=\frac{5+5\sqrt{133}}{6}
$