a(-3a+5a)=7-5a

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

a(-3a+5a)=7-5a

We move all terms to the left:

a(-3a+5a)-(7-5a)=0

We add all the numbers together, and all the variables

a(+2a)-(-5a+7)=0

We multiply parentheses

2a^2-(-5a+7)=0

We get rid of parentheses

2a^2+5a-7=0

a = 2; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·2·(-7)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*2}=\frac{-14}{4}
=-3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*2}=\frac{4}{4}
=1
$