(8x-5)(7x=6)

Solution for (8x-5)(7x=6) equation:

(8x-5)(7x=6)

We move all terms to the left:

(8x-5)(7x-(6))=0

We multiply parentheses ..

(+56x^2-48x-35x+30)=0

We get rid of parentheses

56x^2-48x-35x+30=0

We add all the numbers together, and all the variables

56x^2-83x+30=0

a = 56; b = -83; c = +30;
Δ = b2-4ac
Δ = -832-4·56·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-13}{2*56}=\frac{70}{112}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+13}{2*56}=\frac{96}{112}
=6/7
$