X^2+10x-57=4+57

Solution for X^2+10x-57=4+57 equation:

X^2+10X-57=4+57

We move all terms to the left:

X^2+10X-57-(4+57)=0

We add all the numbers together, and all the variables

X^2+10X-57-61=0

We add all the numbers together, and all the variables

X^2+10X-118=0

a = 1; b = 10; c = -118;
Δ = b2-4ac
Δ = 102-4·1·(-118)
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{143}}{2*1}=\frac{-10-2\sqrt{143}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{143}}{2*1}=\frac{-10+2\sqrt{143}}{2}
$