(7x+6)(4x+9)=10

Solution for (7x+6)(4x+9)=10 equation:

(7x+6)(4x+9)=10

We move all terms to the left:

(7x+6)(4x+9)-(10)=0

We multiply parentheses ..

(+28x^2+63x+24x+54)-10=0

We get rid of parentheses

28x^2+63x+24x+54-10=0

We add all the numbers together, and all the variables

28x^2+87x+44=0

a = 28; b = 87; c = +44;
Δ = b2-4ac
Δ = 872-4·28·44
Δ = 2641
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{-(87)-\sqrt{2641}}{2*28}=\frac{-87-\sqrt{2641}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+\sqrt{2641}}{2*28}=\frac{-87+\sqrt{2641}}{56}
$