2x(x-95)=(x-37)

Solution for 2x(x-95)=(x-37) equation:

2x(x-95)=(x-37)

We move all terms to the left:

2x(x-95)-((x-37))=0

We multiply parentheses

2x^2-190x-((x-37))=0


We calculate terms in parentheses: -((x-37)), so:

(x-37)

We get rid of parentheses

x-37

Back to the equation:

-(x-37)


We get rid of parentheses

2x^2-190x-x+37=0

We add all the numbers together, and all the variables

2x^2-191x+37=0

a = 2; b = -191; c = +37;
Δ = b2-4ac
Δ = -1912-4·2·37
Δ = 36185
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{-(-191)-\sqrt{36185}}{2*2}=\frac{191-\sqrt{36185}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-191)+\sqrt{36185}}{2*2}=\frac{191+\sqrt{36185}}{4}
$