16x(2)=7.5x(2)+17

Solution for 16x(2)=7.5x(2)+17 equation:

16x(2)=7.5x(2)+17

We move all terms to the left:

16x(2)-(7.5x(2)+17)=0

We add all the numbers together, and all the variables

-(+7.5x^2+17)+16x2=0

We add all the numbers together, and all the variables

16x^2-(+7.5x^2+17)=0

We get rid of parentheses

16x^2-7.5x^2-17=0

We add all the numbers together, and all the variables

8.5x^2-17=0

a = 8.5; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·8.5·(-17)
Δ = 578
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:

$\sqrt{\Delta}=\sqrt{578}=\sqrt{289*2}=\sqrt{289}*\sqrt{2}=17\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-17\sqrt{2}}{2*8.5}=\frac{0-17\sqrt{2}}{17}
=-\frac{17\sqrt{2}}{17}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+17\sqrt{2}}{2*8.5}=\frac{0+17\sqrt{2}}{17}
=\frac{17\sqrt{2}}{17}
=\sqrt{2}
$