(4x+6)(5x-4)=74

Solution for (4x+6)(5x-4)=74 equation:

(4x+6)(5x-4)=74

We move all terms to the left:

(4x+6)(5x-4)-(74)=0

We multiply parentheses ..

(+20x^2-16x+30x-24)-74=0

We get rid of parentheses

20x^2-16x+30x-24-74=0

We add all the numbers together, and all the variables

20x^2+14x-98=0

a = 20; b = 14; c = -98;
Δ = b2-4ac
Δ = 142-4·20·(-98)
Δ = 8036
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8036}=\sqrt{196*41}=\sqrt{196}*\sqrt{41}=14\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14\sqrt{41}}{2*20}=\frac{-14-14\sqrt{41}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14\sqrt{41}}{2*20}=\frac{-14+14\sqrt{41}}{40}
$