(2x-3)(x-5)-3=(4x-7)

Solution for (2x-3)(x-5)-3=(4x-7) equation:

(2x-3)(x-5)-3=(4x-7)

We move all terms to the left:

(2x-3)(x-5)-3-((4x-7))=0

We multiply parentheses ..

(+2x^2-10x-3x+15)-((4x-7))-3=0


We calculate terms in parentheses: -((4x-7)), so:

(4x-7)

We get rid of parentheses

4x-7

Back to the equation:

-(4x-7)


We get rid of parentheses

2x^2-10x-3x-4x+15+7-3=0

We add all the numbers together, and all the variables

2x^2-17x+19=0

a = 2; b = -17; c = +19;
Δ = b2-4ac
Δ = -172-4·2·19
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{137}}{2*2}=\frac{17-\sqrt{137}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{137}}{2*2}=\frac{17+\sqrt{137}}{4}
$