(7x+6)(7x-45)=0

Solution for (7x+6)(7x-45)=0 equation:

(7x+6)(7x-45)=0

We multiply parentheses ..

(+49x^2-315x+42x-270)=0

We get rid of parentheses

49x^2-315x+42x-270=0

We add all the numbers together, and all the variables

49x^2-273x-270=0

a = 49; b = -273; c = -270;
Δ = b2-4ac
Δ = -2732-4·49·(-270)
Δ = 127449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{127449}=357$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-273)-357}{2*49}=\frac{-84}{98}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-273)+357}{2*49}=\frac{630}{98}
=6+3/7
$