77=(7x+1)(10x-9)

Solution for 77=(7x+1)(10x-9) equation:

77=(7x+1)(10x-9)

We move all terms to the left:

77-((7x+1)(10x-9))=0

We multiply parentheses ..

-((+70x^2-63x+10x-9))+77=0


We calculate terms in parentheses: -((+70x^2-63x+10x-9)), so:

(+70x^2-63x+10x-9)

We get rid of parentheses

70x^2-63x+10x-9

We add all the numbers together, and all the variables

70x^2-53x-9

Back to the equation:

-(70x^2-53x-9)


We get rid of parentheses

-70x^2+53x+9+77=0

We add all the numbers together, and all the variables

-70x^2+53x+86=0

a = -70; b = 53; c = +86;
Δ = b2-4ac
Δ = 532-4·(-70)·86
Δ = 26889
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{-(53)-\sqrt{26889}}{2*-70}=\frac{-53-\sqrt{26889}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+\sqrt{26889}}{2*-70}=\frac{-53+\sqrt{26889}}{-140}
$