(2x-11)(7x+15)=0

Solution for (2x-11)(7x+15)=0 equation:

(2x-11)(7x+15)=0

We multiply parentheses ..

(+14x^2+30x-77x-165)=0

We get rid of parentheses

14x^2+30x-77x-165=0

We add all the numbers together, and all the variables

14x^2-47x-165=0

a = 14; b = -47; c = -165;
Δ = b2-4ac
Δ = -472-4·14·(-165)
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-107}{2*14}=\frac{-60}{28}
=-2+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+107}{2*14}=\frac{154}{28}
=5+1/2
$