22=x(2x-7)

Solution for 22=x(2x-7) equation:

22=x(2x-7)

We move all terms to the left:

22-(x(2x-7))=0


We calculate terms in parentheses: -(x(2x-7)), so:

x(2x-7)

We multiply parentheses

2x^2-7x

Back to the equation:

-(2x^2-7x)


We get rid of parentheses

-2x^2+7x+22=0

a = -2; b = 7; c = +22;
Δ = b2-4ac
Δ = 72-4·(-2)·22
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-15}{2*-2}=\frac{-22}{-4}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+15}{2*-2}=\frac{8}{-4}
=-2
$