-7x^2+24x+5=3x+5

Solution for -7x^2+24x+5=3x+5 equation:

-7x^2+24x+5=3x+5

We move all terms to the left:

-7x^2+24x+5-(3x+5)=0

We get rid of parentheses

-7x^2+24x-3x-5+5=0

We add all the numbers together, and all the variables

-7x^2+21x=0

a = -7; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-7)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-7}=\frac{-42}{-14}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-7}=\frac{0}{-14}
=0
$