(-7x+41)(-8x+19)=90

Solution for (-7x+41)(-8x+19)=90 equation:

(-7x+41)(-8x+19)=90

We move all terms to the left:

(-7x+41)(-8x+19)-(90)=0

We multiply parentheses ..

(+56x^2-133x-328x+779)-90=0

We get rid of parentheses

56x^2-133x-328x+779-90=0

We add all the numbers together, and all the variables

56x^2-461x+689=0

a = 56; b = -461; c = +689;
Δ = b2-4ac
Δ = -4612-4·56·689
Δ = 58185
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:

$\sqrt{\Delta}=\sqrt{58185}=\sqrt{9*6465}=\sqrt{9}*\sqrt{6465}=3\sqrt{6465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-461)-3\sqrt{6465}}{2*56}=\frac{461-3\sqrt{6465}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-461)+3\sqrt{6465}}{2*56}=\frac{461+3\sqrt{6465}}{112}
$