14-(m+5)=3(5m-3);m=1

Solution for 14-(m+5)=3(5m-3);m=1 equation:

14-(m+5)=3(5m-3)m=1

We move all terms to the left:

14-(m+5)-(3(5m-3)m)=0

We get rid of parentheses

-m-(3(5m-3)m)-5+14=0


We calculate terms in parentheses: -(3(5m-3)m), so:

3(5m-3)m

We multiply parentheses

15m^2-9m

Back to the equation:

-(15m^2-9m)


We add all the numbers together, and all the variables

-1m-(15m^2-9m)+9=0

We get rid of parentheses

-15m^2-1m+9m+9=0

We add all the numbers together, and all the variables

-15m^2+8m+9=0

a = -15; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-15)·9
Δ = 604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{151}}{2*-15}=\frac{-8-2\sqrt{151}}{-30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{151}}{2*-15}=\frac{-8+2\sqrt{151}}{-30}
$