14=7/10*b+8

Solution for 14=7/10*b+8 equation:

14=7/10*b+8

We move all terms to the left:

14-(7/10*b+8)=0


Domain of the equation: 10*b+8)!=0

b∈R


We get rid of parentheses

-7/10*b-8+14=0

We multiply all the terms by the denominator


-8*10*b+14*10*b-7=0

Wy multiply elements

-80b*b+140b*b-7=0

Wy multiply elements

-80b^2+140b^2-7=0

We add all the numbers together, and all the variables

60b^2-7=0

a = 60; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·60·(-7)
Δ = 1680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*60}=\frac{0-4\sqrt{105}}{120}
=-\frac{4\sqrt{105}}{120}
=-\frac{\sqrt{105}}{30}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*60}=\frac{0+4\sqrt{105}}{120}
=\frac{4\sqrt{105}}{120}
=\frac{\sqrt{105}}{30}
$