10x^2-48=-78x

Solution for 10x^2-48=-78x equation:

10x^2-48=-78x

We move all terms to the left:

10x^2-48-(-78x)=0

We get rid of parentheses

10x^2+78x-48=0

a = 10; b = 78; c = -48;
Δ = b2-4ac
Δ = 782-4·10·(-48)
Δ = 8004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8004}=\sqrt{4*2001}=\sqrt{4}*\sqrt{2001}=2\sqrt{2001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{2001}}{2*10}=\frac{-78-2\sqrt{2001}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{2001}}{2*10}=\frac{-78+2\sqrt{2001}}{20}
$