14a(3a-2)=2(2.5a+1)-(a-1)

Solution for 14a(3a-2)=2(2.5a+1)-(a-1) equation:

14a(3a-2)=2(2.5a+1)-(a-1)

We move all terms to the left:

14a(3a-2)-(2(2.5a+1)-(a-1))=0

We multiply parentheses

42a^2-28a-(2(2.5a+1)-(a-1))=0


We calculate terms in parentheses: -(2(2.5a+1)-(a-1)), so:

2(2.5a+1)-(a-1)

We multiply parentheses

4a-(a-1)+2

We get rid of parentheses

4a-a+1+2

We add all the numbers together, and all the variables

3a+3

Back to the equation:

-(3a+3)


We get rid of parentheses

42a^2-28a-3a-3=0

We add all the numbers together, and all the variables

42a^2-31a-3=0

a = 42; b = -31; c = -3;
Δ = b2-4ac
Δ = -312-4·42·(-3)
Δ = 1465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{1465}}{2*42}=\frac{31-\sqrt{1465}}{84}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1465}}{2*42}=\frac{31+\sqrt{1465}}{84}
$