Solve b-3=78,75/b

$$b - 3 = \frac { 78,75 } { b }$$

Solve for b

$$b=10,5$$

$$b=-7,5$$

Steps Using the Quadratic Formula

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$bb+b\left(-3\right)=78,75$$

Multiply b and b to get b^{2}.

$$b^{2}+b\left(-3\right)=78,75$$

Subtract 78,75 from both sides.

$$b^{2}+b\left(-3\right)-78,75=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$b^{2}-3b-78,75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -3 for b, and -78,75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-78,75\right)}}{2}$$

Square -3.

$$b=\frac{-\left(-3\right)±\sqrt{9-4\left(-78,75\right)}}{2}$$

Multiply -4 times -78,75.

$$b=\frac{-\left(-3\right)±\sqrt{9+315}}{2}$$

Add 9 to 315.

$$b=\frac{-\left(-3\right)±\sqrt{324}}{2}$$

Take the square root of 324.

$$b=\frac{-\left(-3\right)±18}{2}$$

The opposite of -3 is 3.

$$b=\frac{3±18}{2}$$

Now solve the equation b=\frac{3±18}{2} when ± is plus. Add 3 to 18.

$$b=\frac{21}{2}$$

Now solve the equation b=\frac{3±18}{2} when ± is minus. Subtract 18 from 3.

$$b=-\frac{15}{2}$$

The equation is now solved.

$$b=\frac{21}{2} b=-\frac{15}{2}$$

Steps for Completing the Square

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$bb+b\left(-3\right)=78,75$$

Multiply b and b to get b^{2}.

$$b^{2}+b\left(-3\right)=78,75$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$b^{2}-3b=78,75$$

Divide -3, the coefficient of the x term, by 2 to get -\frac{3}{2}. Then add the square of -\frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$b^{2}-3b+\left(-\frac{3}{2}\right)^{2}=78,75+\left(-\frac{3}{2}\right)^{2}$$

Square -\frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$b^{2}-3b+\frac{9}{4}=\frac{315+9}{4}$$

Add 78,75 to \frac{9}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$b^{2}-3b+\frac{9}{4}=81$$

Factor b^{2}-3b+\frac{9}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(b-\frac{3}{2}\right)^{2}=81$$

Take the square root of both sides of the equation.

$$\sqrt{\left(b-\frac{3}{2}\right)^{2}}=\sqrt{81}$$

Simplify.

$$b-\frac{3}{2}=9 b-\frac{3}{2}=-9$$

Add \frac{3}{2} to both sides of the equation.

$$b=\frac{21}{2} b=-\frac{15}{2}$$