((x*7)*(x*1.5))=7.5

Solution for ((x*7)*(x*1.5))=7.5 equation:

((x*7)(x*1.5))=7.5

We move all terms to the left:

((x*7)(x*1.5))-(7.5)=0

We add all the numbers together, and all the variables

((+x*7)(+x*1.5))-(7.5)=0

We add all the numbers together, and all the variables

((+x*7)(+x*1.5))-7.5=0

We multiply parentheses ..

((+10.5x^2))-7.5=0


We calculate terms in parentheses: +((+10.5x^2)), so:

(+10.5x^2)

We get rid of parentheses

10.5x^2

Back to the equation:

+(10.5x^2)


We get rid of parentheses

10.5x^2-7.5=0

a = 10.5; b = 0; c = -7.5;
Δ = b2-4ac
Δ = 02-4·10.5·(-7.5)
Δ = 315
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:

$\sqrt{\Delta}=\sqrt{315}=\sqrt{9*35}=\sqrt{9}*\sqrt{35}=3\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{35}}{2*10.5}=\frac{0-3\sqrt{35}}{21}
=-\frac{3\sqrt{35}}{21}
=-\frac{\sqrt{35}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{35}}{2*10.5}=\frac{0+3\sqrt{35}}{21}
=\frac{3\sqrt{35}}{21}
=\frac{\sqrt{35}}{7}
$