(7x-5)(6x+3)=A

Solution for (7x-5)(6x+3)=A equation:

(7x-5)(6x+3)=

We move all terms to the left:

(7x-5)(6x+3)-()=0

We add all the numbers together, and all the variables

(7x-5)(6x+3)=0

We multiply parentheses ..

(+42x^2+21x-30x-15)=0

We get rid of parentheses

42x^2+21x-30x-15=0

We add all the numbers together, and all the variables

42x^2-9x-15=0

a = 42; b = -9; c = -15;
Δ = b2-4ac
Δ = -92-4·42·(-15)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-51}{2*42}=\frac{-42}{84}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+51}{2*42}=\frac{60}{84}
=5/7
$