x(2x-9)=35

Solution for x(2x-9)=35 equation:

x(2x-9)=35

We move all terms to the left:

x(2x-9)-(35)=0

We multiply parentheses

2x^2-9x-35=0

a = 2; b = -9; c = -35;
Δ = b2-4ac
Δ = -92-4·2·(-35)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-19}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+19}{2*2}=\frac{28}{4}
=7
$