96-77x=-15x^2+7x

Solution for 96-77x=-15x^2+7x equation:

96-77x=-15x^2+7x

We move all terms to the left:

96-77x-(-15x^2+7x)=0

We get rid of parentheses

15x^2-7x-77x+96=0

We add all the numbers together, and all the variables

15x^2-84x+96=0

a = 15; b = -84; c = +96;
Δ = b2-4ac
Δ = -842-4·15·96
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-36}{2*15}=\frac{48}{30}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+36}{2*15}=\frac{120}{30}
=4
$