(9.3-x)(6.75-x)2=114

Solution for (9.3-x)(6.75-x)2=114 equation:

(9.3-x)(6.75-x)2=114

We move all terms to the left:

(9.3-x)(6.75-x)2-(114)=0

We add all the numbers together, and all the variables

(-1x+9.3)(-1x+6.75)2-114=0

We multiply parentheses ..

(+x^2-6.75x-9.3x+62.775)2-114=0

We multiply parentheses

2x^2-12x-18x+125.55-114=0

We add all the numbers together, and all the variables

2x^2-30x+11.55=0

a = 2; b = -30; c = +11.55;
Δ = b2-4ac
Δ = -302-4·2·11.55
Δ = 807.6
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{-(-30)-\sqrt{807.6}}{2*2}=\frac{30-\sqrt{807.6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{807.6}}{2*2}=\frac{30+\sqrt{807.6}}{4}
$