5a-7=4(a+1)14a+3

Solution for 5a-7=4(a+1)14a+3 equation:

5a-7=4(a+1)14a+3

We move all terms to the left:

5a-7-(4(a+1)14a+3)=0


We calculate terms in parentheses: -(4(a+1)14a+3), so:

4(a+1)14a+3

We multiply parentheses

56a^2+56a+3

Back to the equation:

-(56a^2+56a+3)


We get rid of parentheses

-56a^2+5a-56a-3-7=0

We add all the numbers together, and all the variables

-56a^2-51a-10=0

a = -56; b = -51; c = -10;
Δ = b2-4ac
Δ = -512-4·(-56)·(-10)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-19}{2*-56}=\frac{32}{-112}
=-2/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+19}{2*-56}=\frac{70}{-112}
=-5/8
$