x(2x-5)=88

Solution for x(2x-5)=88 equation:

x(2x-5)=88

We move all terms to the left:

x(2x-5)-(88)=0

We multiply parentheses

2x^2-5x-88=0

a = 2; b = -5; c = -88;
Δ = b2-4ac
Δ = -52-4·2·(-88)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-27}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+27}{2*2}=\frac{32}{4}
=8
$