(5x+3)(7x+2)=197

Solution for (5x+3)(7x+2)=197 equation:

(5x+3)(7x+2)=197

We move all terms to the left:

(5x+3)(7x+2)-(197)=0

We multiply parentheses ..

(+35x^2+10x+21x+6)-197=0

We get rid of parentheses

35x^2+10x+21x+6-197=0

We add all the numbers together, and all the variables

35x^2+31x-191=0

a = 35; b = 31; c = -191;
Δ = b2-4ac
Δ = 312-4·35·(-191)
Δ = 27701
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{-(31)-\sqrt{27701}}{2*35}=\frac{-31-\sqrt{27701}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{27701}}{2*35}=\frac{-31+\sqrt{27701}}{70}
$