(5x-7)(10x=1)

Solution for (5x-7)(10x=1) equation:

(5x-7)(10x=1)

We move all terms to the left:

(5x-7)(10x-(1))=0

We multiply parentheses ..

(+50x^2-5x-70x+7)=0

We get rid of parentheses

50x^2-5x-70x+7=0

We add all the numbers together, and all the variables

50x^2-75x+7=0

a = 50; b = -75; c = +7;
Δ = b2-4ac
Δ = -752-4·50·7
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-65}{2*50}=\frac{10}{100}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+65}{2*50}=\frac{140}{100}
=1+2/5
$