(x-6)(2x-7)=

Solution for (x-6)(2x-7)= equation:

(x-6)(2x-7)=

We move all terms to the left:

(x-6)(2x-7)-()=0

We add all the numbers together, and all the variables

(x-6)(2x-7)=0

We multiply parentheses ..

(+2x^2-7x-12x+42)=0

We get rid of parentheses

2x^2-7x-12x+42=0

We add all the numbers together, and all the variables

2x^2-19x+42=0

a = 2; b = -19; c = +42;
Δ = b2-4ac
Δ = -192-4·2·42
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-5}{2*2}=\frac{14}{4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+5}{2*2}=\frac{24}{4}
=6
$