(4.20x-5.80)(7.20x-9.20)=9.10x+9.50

Solution for (4.20x-5.80)(7.20x-9.20)=9.10x+9.50 equation:

(4.20x-5.80)(7.20x-9.20)=9.10x+9.50

We move all terms to the left:

(4.20x-5.80)(7.20x-9.20)-(9.10x+9.50)=0

We add all the numbers together, and all the variables

(4.20x-5.8)(7.20x-9.2)-(9.10x+9.5)=0

We get rid of parentheses

(4.20x-5.8)(7.20x-9.2)-9.10x-9.5=0

We multiply parentheses ..

(+28x^2-36.8x-40.6x+53.36)-9.10x-9.5=0

We add all the numbers together, and all the variables

(+28x^2-36.8x-40.6x+53.36)-9.1x-9.5=0

We get rid of parentheses

28x^2-36.8x-40.6x-9.1x+53.36-9.5=0

We add all the numbers together, and all the variables

28x^2-86.5x+43.86=0

a = 28; b = -86.5; c = +43.86;
Δ = b2-4ac
Δ = -86.52-4·28·43.86
Δ = 2569.93
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{-(-86.5)-\sqrt{2569.93}}{2*28}=\frac{86.5-\sqrt{2569.93}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86.5)+\sqrt{2569.93}}{2*28}=\frac{86.5+\sqrt{2569.93}}{56}
$