2.5x(x-7)=2x-23

Solution for 2.5x(x-7)=2x-23 equation:

2.5x(x-7)=2x-23

We move all terms to the left:

2.5x(x-7)-(2x-23)=0

We multiply parentheses

2x^2-14x-(2x-23)=0

We get rid of parentheses

2x^2-14x-2x+23=0

We add all the numbers together, and all the variables

2x^2-16x+23=0

a = 2; b = -16; c = +23;
Δ = b2-4ac
Δ = -162-4·2·23
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{2}}{2*2}=\frac{16-6\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{2}}{2*2}=\frac{16+6\sqrt{2}}{4}
$